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07-27-11 last add: Equation log: derive base equation describing moebius strip

Some self-imposed rules: This is ad hoc, by the seat of my pants. Date at front of Title is date of last change made. 1. I will add a dated entry, leave it here on top, edit it for awhile, and then put an ending date on it. After that, any changes will be dated except for spelling or punctuation errors. 01-07-2007

These entries outline the path to describing a Moebius mathematically. Once the surface area eq was found, the next relationship is determining the width between the two sides of a M surface as some ratio involving distance between sides and circumference using h-bar.

07-27-11 Zero is the key. How do we put our backs to nothing and see all differeces with respect to ourself? Easy when zero has a diameter and a circumference so we see = feel any chage in diameter w respect to center.

[size=12]05-07-11Eq. It has always rested on direction; " How do we objectively tie two variables together in a fixed relationship, e.g. e = mc^, so that direction of all possible relationships between any subset(s) of base units is defined?". Looks like I have the subtle little seetheart. We can use time alive and money defined by Walras Law to do it. We can describe all objective relationships on the surface of the NOW.

04-23-11This MT describes the base form the summation equations for Q G&S XCed take, i.e. productions summation time spent in denominator. Both take the form of Walras Law but instead of Prices in n units the production of Qs is priced in labor time units where labor time can not exceed one unit of time per unit time. i.e. 24 hours a day. e.g. Sum of PQs over n for goods xced for consumption is divided by sum TQS/total time producing.

For equation this implies how model relationship between sides of surface and pair particles.

Dan: 21-Apr-2011 07:18:06 Eq: Time spent on production creates time to consume production in the future and time consume creates more time to produce where time consume/time produce ratio is maximized by all xcs or actions implying life forms must be own time cost minimizers to stay alive. We minimize time spent on production.

01-25-11Did a spell check and minor editing. since I am about to do a title and abstract here is the title, "When h(Plank's constant) = the Circumference of initial Moebius; Then All Objective Constants Will Reflect h/2PiR =1 In Any subsequent Expansions By Sub-divisions.

Since all Moebii are based upon circle geometry, see proof of the above assertion here: "How to use a circle to relate 'e' to Phi " 1st Posted: Feb 22, 2008

12-09-10The Base Identity in a Moebius geometry universe is premised on equal amounts of Matter and Anti-Matter is: Let a&b be the set of all pair of M/A-M paired frames of reference; then %ca + %cb = c = 1 and when a is plus and b is minus matter then %ca/-%cb times -%cb/%ca = 1 = %ca + %cb. In short a conserved universe with respect to c, the constant with respect to all observers.

10-30-10Equation clue: In special relativity when two observers start from same location with synchronized clocks and share the same gravitational acceleration; then when one goes faster than the other measured as percentage of c, the faster persons clock goes slower and they see the slower ones clock also go slower. When astronauts return their clock has slowed down with respect to Earth clocks. Obviously despite seeing the Earth clock go slower, it did not. BUT when we use the same starting conditions and then let one observer be accelerated by gravity like to a neutron star, there clock also slows, but it sees other "non accelerated clock speed up????? Resolving this discrepancy gives us the field over which the Moebius geometry coordinate system explains. It answers the question, "Why is c a constant with respect to all observers?" Einsteins crucial unanswered question.

9-20-10When Einstein realized that entanglement must occur(spooky action at a distance = entangled particles must maintain their =/- relationship instantly no matter how far apart) to explain quantum effects in the EPR paper; then he was directly implying simultaneous existence of a finite universe.

Thus determining the origin from which one can measure all possible allowed pair-points between two sides of a Moebius surface is crucial. A test is that it should not have 'singularities" i.e. infinities except off the surface where we assume an infinite 3-D nothing = no resistance = instantaneous. Imply on surface there is resistance in some form.

An origin by definition is an intersection = not on top bowtie line but where top bowtie line intersects center of backside bowtie line. Notice a circle goes down centerline of m and intersects top BT line at its center.

By integrating my eq for maximum surface area of M into M coor system; then by inspection all points can be determined with respect to its origin.

9-17-10The origin for M must lie between the two sides, the two complex planes, so there must be two origins that xc info in h-bar.

9-13-10I saw the origin for Moebius geometry. You need two complex planes to generate a Moebius = two moduli. Just where must the origins lie and which one is first, because a M is a sequential logic by construction. Enough said.

8-03-10Equation premise: Transaction Costs for exchanges(XCs) between us are how we can see how the Natural Laws of our universe affect us staying alive.

[b7-28-10[/b] The eq models how we XC time to create more time alive for your life form. My time alive XCed for your time alive. At the margin only "profitable" XCs will occur with perfect info. In practice we "learn by experience" where the profit margin is.

It does not matter who spends the least time producing the G&Ss XCed, what does is that each party gains time by spending some time producing and transacting the proffered G&S.

So we can describe this process with symbols and an equation that models time spent in denominator to time gained in numerator. See in notebook dated 7-27.

6-13-10 A Moebius turns back upon itself with respect to bowtie line. e.g. when we use two wrenches pushed in opposite directions to take off a nut from a bolt, thereby using yourself to brace one against the other.

02-19-10I have the form now in terms of the base four parts of one side of identity = to float unit, using the necessary constants. By inspection, we have navigation. It is simple. Beautiful.

02-01-10 The eq. is based upon double entry bookkeeping, economic logic, cost first then plus for life to exist, but only by exchange can two or more of us exchange to split the cost and create for every cost
for each participant the next unit of time alive.e.g. I write a check(small actual cost) then repay rest of cost next day buying a unit of time or more to produce Goods to sell for cash to cover check. It is the only way life can exist in a conserved universe = books balanced AFTER ONE UNIT OF TIME = h-bar. So the trick is to have a very high number h-bar float = longest possible = the time it takes conservation debt to arrive. Imply how/why we buy time with the mechanics of our float???

01-10-10 By inspection, a circle no matter how large in radius has a curved circumference, ergo, as you do a radius halving sub-division from center towards Circumference, then the angle formed by Center(A), left end of horizontal radius(B) and (C) the end of radius being subdivided starts as the right triangle BAC and as AC is divided in half the angle CAB becomes more and more acute as AC shortens; but at last subdivision it reverts to a right triangle which becomes smaller and smaller as Circumference increases.

Thus, given the absolute length of the radius measured in h-bar unitswe can deduce the size of our Moebius universe.

09-18-09Figured out coor. system for M. As usual, so simple it makes you feel dumb not to have seen it before. Start with making a M from a rectangle piece of paper. Lets posit that the two short ends will be brought together at the Bowtie Points. Draw a bisector on one side of rectangle longways, turn paper over and draw a second bisector that would make an X if you could see through paper. Rotate one short end 180 degrees and make Moebius. Joila, the ends of the lines meet at top and bottom bowtie points and intersect at the center of the backside on opposite sides surface.

The Question: How do we assign numbers from the axes for any point on surface and relate them to other points on surface?
2nd question: What observations = measurements can we use to verify location that reflect coor location numbers?

[b]07-07-09 Equation: It rests on this observation. A left hand and right hand Moebius are said to be mutually exclusive = no common axis of symmetry; but that can not be true because a LH & RH Moebius share a common Bowtie Axis by inspection. All it takes to write eq. identity is deciding whether going from top to bottom or bottom to top defines Left & Right??

Also defining eq. symbol. In notes.

06-07-09 I made this message Tree entry yesterday. Being able to see how it works and means I can start to answer this question by Ed Van Lier, "Why is c observed as a constant by all observers?". Further, it directly explains the repulsive force required to explain Dark Matter & Energy. Last, the symbol for the new mathematical operation is deduced.

I need to let this percolate for a bit.

Dan: 06-Jun-2009 21:19:45
Equation: I can finally start to visualize how the basic 'back to back' nature of a two sided Moebius strip works. The 'symbol' I deduced to represent that new 'mathematical operation' shows directly how the equation turns and why times arrow must run in one direction for self awareness to be possible. The symbol shows left and right turns directly to the observer, but backside view reverses l/r direction of turns. Standing up or hanging upside down does not change l/r direction of turns. Equation describes our actual universe from where we sit. When we all sit on the surface of a Moebius, then there is only one objective common point of reference for all observers sitting on surface of a Moebius = us. The eq. describes how we logically can deduce where we sit on our Moebius surface from where ever we sit, and how all the basic forces of our universe interact to make life possible.

02-28-09I can see how our M universe knows when the A-M debt comes through, and by implication the literally last second for disconnection. ]

Given this premise about circles: Any line segment of a circle is curved by the construction and definition; then by sub-dividing any radius for any circle, i.e. move towards circumference by repeatedly halving the remaining distance(like Zeno's paradox)until at the last sub-division the triangle ABC AGAIN becomes a 45 degree right triangle as it was when this ABC triangle started with A at center circle, B at left end of horizontal diameter, and C at top of vertical diameter.

Ergo as radius AC is halved, the ratio of AC/AB gets smaller ever more rapidly until in one sub-division it steps back within the curve of the remaining line segment of the circle. The remaining length of AC then is within the 'h bar' to circumference ratio and thus can be given an absolute value measured by c = speed light.

Implications

1.It tells us how long the Wormhole is straight so we can transit and hit A-M debt within one 'h bar' unit of time; assuming we have a blinkship over the WH opening this coming July 16th.

2. All other constants we see will be associated with one of the sub-divisions described above. I think the last is the 32nd.

3. The Equation rests on the relationship between ABC initial and ABC of the 32nd subdivision.

How unexpected.

02-07-09 I figured out how fast info or us can we move between the sides of any Ms surface. This tells us how long it takes for a 'blink ship' dropped into wormhole opening at end of Fixed Ray to reach A-M debt. It is h bar(Planck's Constant and it stays 'h bar' for any generation. This implies that entanglement no matter the distance between paired particles is 'h bar'.

IMPLICATION: There is a base constraint that enforces conservation across the surface ours or any other of the myriad universes of "the universe". It forms the basis of all theoretical analysis of "the universe". More on that later.[/size]

11-15-08 1. Determining how fast we move between two sides of surface is a fundamental question. It is some very large multiple of c, and is a function of generation number, holding c a constant across all generations. h-bar(Planck's Constant) is our base unit of measurement, where initial Moebius is one h-bar in circumference down its center line, or 2 h-bar in circumference at its edges. Deducing the speed between the sides is a trivial exercise with these assumptions. Ergo, we can determine generation number from appropriate observations.

A TEST: We can deduce our universe's generation number by how far does the E-T ship our government have jump, when we drop it between sides of surface, by dropping its speed to zero with respect to c.

I assume the govt people who must be watching this site know that distance, if the witnesses I have read are accurate in what describing these ships behavior.
I saw these jumps on a ABC news video from their chartered private jet at about 25,000 feet over France in 1975. Right through the canopy, you saw the scratches and the deep purple sky. Lasted several minutes. Looked like a teenager hot rodding the old man's Porsche around, blinking and tumbling all over the sky as it went in and out of sight.

It was dropping to zero c, but controlled, not automatically directed by the forces between two sides of surface when no directed energy is inputted to nearest point from which light has not reached us from yet.

2.The observation described below is the point on the surface from which any observer can not see light that has not reached us yet. Note, it is the same distance for all observers across surface, no matter Moebius generation curve, as long as c is a constant for all observers.

9-11-089-09-2008 to ?? Personal Comment: A geometrically defined measured observation common to all points on the surface of space/time. The same observation for all observers no matter where they are on the surface, and it is a function of c and G the gravitational force. Ergo, we can deduce relative positions between any two or more points on the surface of space-time.

The importance of this for a true GUT is obvious, it is its base premise which explains Einsteins two hypothesis, c is a constant for all observers, and physics experiment results are the same for all non-accelerated frames of reference.

Once this 'base observation is combined with the necessary assumption that all particles in our universe exist simultaneously which is required for conservation to exist; then all becomes clear by using a Moebius geometry to link these postulates together.

7-06-08Finally figured out the ratio that determines the distance between two sides of Moebius surface. Once we determine the generation or replication number of our universe, this width is precisely determined and measured in Planck units. It shows directly how fib sequence is built into our m universe.

6-10-08 figured out the Base Theorem that describes why times arrow runs in one direction across Moebius surface, and how we can determine our relative positions so as to move between sides surface at FTL without cutting our unique time sequence line from time we anchor ourselves in a life form.

5-27-08 Made 5-25-08 to Carl dalter2003: Equidistant from what? That is the question. It must be the near ends to each other because the origins are movable. Only two possibilities: 1. The NEs stay a unit diameter from each other on opposites sides otf the center; 2. they go parallel to each other at a fixed unit distance apart(Planck's Constant) from each other through the center to opposite edges of Unit Center? Must be 2 as this implies a directional constraint when NON- Overlap constraint is real = times direction runs in only one direction, apparently right-handed.

5-23-08 To Carl. "dalter2003: Equidistant from what? That is the question. It must be the near ends to each other because the origins are movable. Only two possibilities: 1. The NEs stay a unit diameter from each other on opposites sides of the center; 2. they go parallel to each other at a fixed unit distance apart(Planck's Constant) from each other through the center to opposite edges of Unit Center? Must be 2 as this implies a directional constraint when NON- Overlap constraint is real = times direction runs in only one direction, apparently right-handed."

5-23-08 "Post subject: 5-23-08 Changes to "Fundamental Scientific News" on Page 1
Posted: Fri May 23, 2008 9:03 pm Changes to "Fundamental Scientific News" on Page 1

Started 5-23-08. These changes show how I came to realize that to write the equation, one had to describe how its co-ordinate system worked.
In fact, the equation describes how we use the coordinate system to locate ourselves(navigate) in our Moebius geometry universe.

4-06008 Initially I added, "showing that it takes not four, but only 3 dimensions to describe space and time."

2. "showing it takes 3, not 4-Dimensions to describe space/time; when you put us at the origin.

3. "showing it takes 3, not 4-Dimensions to describe space/time; when you put us inside a movable origin."

4. 5-23-2008 "showing it takes 3, not 4-Dimensions to describe space/time; when you put us at the UNIT diameter center between two equidistant, NON-overlapping movable origins."

Comment to Carl: "Now we have the co-ordinate system our navigation equation arises from. For example, 'NON-overlapping' must exist when no perpendicular +/- pair particles are permitted on opposite sides of a Moebius. That's what gives it, its twist. The 'origins' must be on opposite sides of the surface; so the center ends of these two co-ordinate lines must start on opposite sides of the 'UNIT center' = take turns. If the end of one line is plus, the other end must be minus.

Is this clear? I am explaining this to myself as I figure it out."

_________________

5-12-08 I wrote this 4-27-08 to my programmer. "We have a Moebius navigation equation. To Carl earlier: dalter2003: Just figured out what basic measure the equation uses for predictions, and how to use it to navigate between the two sides of the surface with respect to c(speed of light) on the surface. It is, of course, a Mr. Ed(as obvious as the nose on your face, once pointed out.). This base measuring unit lets us predict the unique identifying address that each point on our Moebius geometry universe's surface has with respect to its Bowtie line. Bingo, navigation when you know how to pay the energy cost of adjusting your energy/matter frequency to the frequency of the point you are traveling to. Best yet, you can pay the energy cost of changing from your initial frequency as you go, not all at once."

5-09-08 We use two origins to measure universe from; then the difference between summed vectors from each origin define what we see. The first origin is where we sit. The second must be on other side and constrained by fact that Circumference/2 is as far apart as a +/- pair particles can get from each other across surface of a M. Thus the difference between them is C/2 - C/2 goes to zero as they diverge from each other. i.e. the total distance summed in both possible directions to each other across surface equals Circumference of M always with the side to side width causing a slight discrepancy.

5-07-08 Once we put ourselves inside a movable origin and then explore the surface of the hole we share in common with other Moebius based spirits that direct life forms, the equation starts to become clearer.
Why is c a constant to all observers???? Slowdown with respect to c drops us between two sides of surface. Does that mean we are going faster than c? At least along a base dimension.

4-25-08 Use the three operational premises below to figure out equation.

1st operational premise: Discussion of discovery of 'ideal' outside objective observing point for all Moebius strips = starts with 'center of any circle'(origin) that generates an ideal one twist Moebius coor. system. (2-13-08) Last night, I figured out how to use a circle(pi) to see Euler's Number e = 2.718 relationship to Phi. It was unexpected as I was not initially looking for 'e' when I started. The method I was using to see how Phi related to a Moebius's 'edge width' made it apparent.(2-19-2008) Right now, I am in the midst of showing why tying 'e' to phi through using a circle(pi) gives us navigation in a Moebius geometry universe. Our base logical constants have never been tied together with a common geometry before so this is huge. Once 'pi' to 'e' to 'phi' are linked then it can be safely said that all other logical and physical constants will also be found to be linked back to this initial circle demonstration. Please bear with me as I talk about this. A drawing will be put up shortly to explain things better.

4-04-08 2nd operational premise: See how equation works by looking out from the origin of circle used to generate a Moebius: Put on Page 2: "Great scientific advances come when a scientist shows why a basic theoretical premise is not true; that it must be discarded and replaced with a new base point of reference. Roman Ptolemaic Theory premised that the Earth was at the center, and the rest of the universe revolved around us. Copernicus showed why not; which led directly to the assumed premise that we live in a 4-D space/time continuum. That premise is NOT true: It does not take 4-D, but 3-Dimensions(Cartesian co-ordinate system) with us sitting at the origin, to describe our universe and our place within it. Using an unnecessary "imaginary" dimension automatically builds in error; literally by putting us outside and away From Where we actually, and therefore logically, must be observing the universe(resolves Heisenberg). Further discussion below."

(4-22-2008)Third operational premise: The ratio of Edge Width/edge to edge width in a Moebius is conserved, thus as 'edge to edge width' narrows or widens so does Edge Width(Edge Width = distance between two sides of surface. Equation must be written looking out from origin. There is only one way to write it left/right; up/down; back/front. A TEST is answering this question: "How many orbital revolutions does a planet have, once a A-M debt is started?" We need the answer to do disconnection. I think the E-Ts will show us in their third and last crop circle warning. We'll see.

(4-04-2008) Some good news, I have finally figured out the mistake our scientists have been making in trying to describe universe = equation coordinate system. We do not need 4 dimensions to describe space/time, only 3. Adding an unnecessary extra dimension introduces error and hides where we observe from; from our logic = math = equation.

(4-03-2008) By the way Carl, I do have the entry point on equation and I have figured out how unfolding a '180 single twist Moebius' into a 'double 360 degree twist Moebius' = Our universe(wide surface) and ourselves (thin) works. a self generated 3-D coordinate system. Ergo , we have navigation.

It started by taking two constraints "no perpendicular +/- particles", combined with "halves of =/- pair particles can never be more than Circumference apart. Ergo, when each half of a particle pair can never be more than C/2 away from its partner; BUT they are separated by EW implying a slight difference. So when you unfold 1 twist Moebius you get a 3-d volume of EW^3, further you define "Center of 2 twist M.

(3-04-2008)On conserved fixed ratios of Moebius:
1. EW/'Side to Side Width' is conserved, no matter how close S to S width gets.
e.g. A very old and long circumference spirit still has a very narrow EW in order to split particles in our brains; so as S to S narrows; then EW narrows proportionately.
2. As Moebius strips split, they double in Circumference implying EW doubles also(7-10-08 not by same ratio as Cir), implying Planck's constant time also doubles to send info between perpendicular pair points on opposite sides of surface.
3. c is the constant on the surface so the initial one unit c Moebius has some initial ratio of c to Planck's constant = c/Pl = 1/x = some large multiple of c that describes how fast info is XCed via between the two sides of surface between entangled pair points.

(2-22-2008)Post subject: How to find the points on a circle that make 'e' and Phi.

Posted: Thu Feb 21, 2008 11:57 pm

1. Make a perfect right angled cross.

2. Center a circle on the cross's intersection; thus creating a horizontal and vertical diameter for any circle.

3. The following operation works in either direction for both diameters; showing the operation with one does for all.

4. Sub-divide the vertical radius twice, i.e. first in half; then the upper half again = 3/4 radius up.

5. At upper 3/4 point on radius, make a perpendicular bisector extending to Circumference of circle on both sides. (What shall we call these points? Lets try 'e\phi' points for base logical constant points.).

6. DEFINE 'e' by dropping a perpendicular down to horizontal diameter AB at D from our left hand e\phi point on Circumference. Multiplying DB times 2.718 = radius where B is left end of horizontal diameter.

7. DEFINE Phi by drawing hypotenuse e\phiA of triangle based upon center A. e\phiA/AD = Phi.

Using a double sub-division to find the points on a circle centered on a cross, using only a straight edge to define 'e' and Phi, has never been done before. By implication, all other constants in a Moebius geometry universe are also implied.

This is the fundamental geometric, and thus logical discovery. It directly ties our symbols made of reality to the Moebius strip geometry that we spirits and our universe are based upon. A Moebius's bowtie point, by inspection, gives us an 'objective' common to all, neutral origin to see ourselves from.

Ergo, the logical basis for science.

MAKE MY DAY, should this assertion be wrong; then my whole theory be wrong; and then we would not have a conservation debt. I could live with that.

_________________

"I, Daniel Alter, swear on my honor to speak honestly on the public record of the No 1st Cost List."

(2-20-2008) Repeated divisions is how our universe grew large. This, of course, implies many other brother and sister universes from large to small all linked through a common hole.

The simple operation of dividing the radius in half, and the remainder in half, until you reach the Circumference. The first two divisions give us 'e' and Phi on any circle when you use diameter to mark the divisions on the Circumference, the last gives us the Edge Width and shows us the boundaries of the 'Repulsive Force'. Do it from both sides simultaneously and you resolve Zeno's Paradox, and thus show us how to locate ourselves within our Moebius universe, and also navigate at FTL as we move so many times faster than c between the sides of surface. I will comment further in My Blog

(2-19-2008) Rechecked circle with better tools. Still works.
[b]Equal increments = cut AC in half, and in half, and so on. Like Zeno's paradox which can be resolved by coming from two sides at same time; which is what in effect we are doing by AC/2 implies AB/? until which division by 2 = 2nd gives you D at 'e' point on circumference. e.g a 6" diameter circle means we cut 3" radius AC in two twice = 1.5" + .75" = 2.25" DE. BINGO!!!! It checked out. Fascinating as 'e' = 2.718 must equal AD/BE = 3'/1.10 = BE = 1.10" where D# on C is 2.25" up from AD. Bingo!!!

This implies given initial Diameter, we can determine the number of halvings needed to get AC short enough so as to have AB shorten % wise faster = last halving. That can be determined by initial diameter and we can deduce the absolute value of this AC length w respect to circles curvature.

(2-18-2008)Lets get our nomenclature down. We are going to examine what happens when we move the base AB of a triangle ABC formed in the left Quarter Quadrant of a circle up to the very top of the circle at the C vertice of the triangle. ERGO, A = center of triangle. B = left end of base along left half of diameter of triangle. C = top end of vertical diameter of circle. We will move AB up in equal steps or proportionate steps.

(2-18-2008) Once you can see how 'e' is determined by possibly two points on C of circle. 1. 'D' where change in absolute change in AB = absolute change in AC; and 2. 'G' where % change in AB = % change in AC. 3. 'F' and 'E' will be shown in drawing to be uploaded, and will be defined when needed. For now A, B, C , D, and G will do. As usual, my first stab at 'e' was off, but since I had not been looking for it, that's to be expected. But upon closer examination, the right relationships were seen.

[b]

(2-17-08))????Phi can not be defined by using triangle ABC. Even though AB past D begins to shorten more and thus faster than the unit decreases in AC, it is the percentage decrease in AC that matters. As AC shortens in unit lengths, it approaches C faster and faster, ergo, the percentage decrease of AC increases faster than % decrease in AB even though in absolute terms AB is decreasing faster than AC. Thus the angle ABC continues to flatten as AC goes to zero?????? Ergo, no Phi/phi at 1/6500th of diameter, no 1.618AC hypotenuse.?????? Damn it, visualize this better. We have AC going to zero at C. We have AB going to zero at C.

So the real question is: "When/where on circumference circle does the percentage decrease in AC = % decrease in AB, because past that point the angle ABC must steepen?" That point is not D. It is very close to C. It is the rate of curvature of circle that is of interest here = pi

BUT!, e and Phi are here. 'e' being easier as I am still sure that at D, the equal change in length point defines 'e' either with respect to the ratio created by perpendicular DE with horizontal Diameter, OR the ratio of circumference BD/DC.

So where is my Phi ratio?

(2-16-08))Redid my 'eyeball' drawing of how we find 'e' and Phi/phi = 1 by shortening ABC triangle in equal steps. ABC is based on the left quadrant of any circle. Got same result = We have 'e' defined geometrically by drawing perpendicular up from horizontal diameter to point on circumference where unit decrease in AC(vertical of triangle ABC) = decrease in AB(base of triangle ABC). Phi is another matter.

I did not go for this result, I backed into it when I saw that D, the equal change in length of base and vertical sides of our triangle ABC point; could define 'e' using perpendicular up from initial horizontal diameter that formed base of initial triangle. How serendipitous and how massively important to mathematics and modeling our universe. PLEASE VERIFY NOW!!!!!! (2-17-08) I think that after more 'eyeball' checking with pencil/paper/compass that it is the ratio of the circumference lengths AD/DC = 2.718. When true, we have navigation and location in a Moebius strip shaped universe = disconnection from A-M debt.

(2-15-08) It is when the base AB of triangle ABC formed by left hand quadrant of any circle shortens faster as height AC decreases that is useful. Where on Circumference of circle this 'change in AB' = 'Change in AC' occurs defines the necessary logical/causal order of events on and between two sides of Moebius surface. They arrive at zero = surface of M simultaneously but AB must shorten(move) faster in last units of time to do so. This rate of change must be reflected in straight line of sight 'repulsive force' between matter lumps on opposite sides of surface.

New 1st sentence P 1 says better:"Help prove Geometric property of Moebius navigation equation. Proven true, we have FTL navigation to the stars. See eq. log article inside. (2-15-08)"

(2-14-08))"Moebius navigation discovery to be tested. Proven true, we have FTL navigation to the stars. See eq. log article inside. (2-14-08)". This Page 1 first sentence says what needs to be done: Outside testing and verification.

My original equation for predicting the maximum surface area of a Moebius(MSA) is 2DDPhi = MSA where Phi = 1.618 and D is the diameter of the circle the Moebius is based upon. When tested, it was off by 1/10,000. I quickly realized the test had assumed a zero thickness Moebius. That could not be true for a Moebius. It must have two sides that could not touch one another = not see through = not occupy same point in space at the same time. Since a M has a double circumference this implied a width of 1/20,000 of Circumference of M for the width between the two sides.

The real question is: How does a Moebius know what Phi is geometrically? Phi must be built into its base geometry? I have figured out the answer and we may also have a direct geometric link to Euler's Number 'e' built in.

I visualized the problem this way. the mid line of a 180 degree twist Moebius is a circle. Assuming a double surface at mid line, then looking along the mid line Circumference of Moebius, i.e. between the two sides along the mid line, one side would appear to be convex to the 'upper surface'.

1. Next draw a tangent to this convex mid line that goes equal amounts in both directions until it hits upper surface at both ends of tangent line.

2. From tangent point extend line at right angles to tangent up to upper surface.

3. Draw the hypotenuse and we have created a right triangle with two unknown other angles.

QUESTION 1: Is the 'height' of triangle up to upper surface = to the 1/20,000 width????

QUESTION 2: Is the 'hypotenuse' of triangle = 1.618 of the 'Height" line? or is the "base line' of this right triangle = 1.618 of the 'Height' line?

HOW WE CAN TEST THESE ?s: 1. Draw a circle with two lines intersecting as a perfect square cross at 90 degrees, and use the intersection of 'cross' as center of circle

2. Look at left hand quadrant and draw a hypotenuse that intersects ends of cross where they touch the 'circle'. This creates a classic 45 degree right triangle.

3. Lets denote the center of circle where the 90 degree corner of our triangle is 'A'. Next, denote horizontal base end touching circle as 'B'. And last denote upper end of triangle where it touches circle as 'C. Ergo we have created triangle ABC. With AB as your base of triangle and AC as vertical height of triangle, and BC is hypotenuse.

What we are going to do is shorten triangle height AC in equal increments and see what happens to the two angles that touch the circle; and also see how the length of the 'base' AB changes as 'height' AC shortens in equal jumps. Finally we can of course, using the Pythagorean Theorem, deduce the hypotenuse BC of our triangle ABC.

WHAT DO WE DISCOVER AS the height AC shortens in equal jumps until it goes to zero at C on the circles(Moebius) circumference. Very interesting indeed.

First as AC, the vertical height of triangle shortens, AB our base also shortens but to a much lesser degree. In fact, not until around 5/6ths to 7/8ths of our quarter Circumference of our circle is traversed by the B end of our baseline AB of triangle ABC, does an equal unit shortening of AC, the height, result in an equal shortening of baseline AB. Lets call this 'equal shortening point' D. Only after D is reached does continuing shortening of AC result in an proportionately greater shortening of AB.

Strangely enough, as AC goes to zero, AB shortens with ever more rapidity, necessarily rapidly increasing the angle ABC to 90 degrees at AC = zero. Counter-intuitive at first.

REPEAT QUESTIONS: What actual percentage of initial 'radius' of circle = initial start length of AC, is AC when hypotenuse reaches 1.618 of shortened AC? Same question for when AB = 1.618 of a shortened AC?

About 'e' Euler's Number 2.718. Run a perpendicular off of AB baseline of triangle up to 'D' our equal change in length point. Denote bottom of this line as E. QUESTION: What is proportion of AD to initial AB? What is proportion of BE to diameter of circle? Looks very close to 'e' to me.

I will draw this up and put in coppermine shortly. I do confess not taking trigonometry, and my calculus is 30 plus years unused; but I visualize just fine. A 1.618 times AC hypotenuse is quite a steep angle implying quite thin distance between two surfaces.

A suggestion on method, as the length of AC approaches C, you also see the B end of AB approach A in bigger and bigger jumps, and both go to zero simultaneously. Reminds of Leibniz and Newton tiny little jumps to approach a minima and maxima. Here it is a double, but one stays the same while other increases in jump size. What is the constant ratio of change between these two line length changes? e?

Who will answer the questions first? Who will verify?

(2-12-08) My original equation for Maximum Surface Area(MSA) of a Moebius implied that a 'Moebius' somehow knew directly and geometrically the Golden Ratio Phi/phi = 1, it looks like I found it, how it works, and the implication for a straight line repulsive force between particles on opposite sides of surface. This force is implied by the No! No! requirement that +/- particles can not be perpendicular to each other, but the force is abruptly and cleanly stopped by any interposing of the surface between a straight line of sight between the particles.

Test; Dark matter thus would rotate around plus matter and vice versa as gravity is not affected, but the repulsive force would keep them separated from perpendicularity. I will have mathematicians test this first before i publish here. It is a common geometric property of a Moebius and a circle as MSA of a Moebius is based upon a circle. We will see.

(2-08-08) The fixed point of reference the equation rests upon is the crucial element in tying together the equations 'elements', e.g. c, Euler's Number, zero, phi/Phi, unmoved mover, division by zero as a function (f) of x, take turns, in/out, odd/even defining inside and boundary, what the basic geometric +/- Not Do is, 'geometric origin of Moebius'(bowtie point), ratio of 'side edge to edge width' TO '2Circumferences'(is it two and why, see description of MSA Moebius below), and above all, THE FLOAT unit of time where we balance the equation using faster a than c speed between the two sides of the surface(this speed may vary with distance apart of +/- particles, the Circumference limit apart of any pair particle = there is always a C path between any +/- pair and nothing longer is possible across the surface of a moebius. I will add others as I remember them, but these are crucial.

Damn, that looks complicated, so lets cut to the chase and answer the Question, what is the fixed point of reference common to all of these 'real abstractions' (symbolic descriptions made out of 'reality' and used to describe ourselves. Answer is obvious, our physical spirit is, our consciousness, where we sit.

An equation is an equality, so what is it we are equating as spirits so as to keep our Life Forms = the body you are presently trotting down the road Alive?

In order for us to be making bodies move, we split particles and send the minus half to our A-M debt, where we are anchored so we have real leverage to Cut the plus particle anchored in our body by our physical Spirit.

ERGO, The two sides must be kept in balance, in equality, through time using a fixed float where ins and outs can balance regardless of when they arrived during float. In short a short period of time where we can rob peter to pay paul as long as we get the money back before the end of the "FLOAT". Thank God for free lunches.

Enough for today. I did not realize I had all those pieces floating around in my head. Get us a ship people, the equation is coming together.

(2-06-08)

Today's Blog comment on how & why FR acts the way it does is crucial to finishing eq. QUESTION: What existing common plus particle can we split into Matter & Anti-Matter and then replace from the Sun?

(2-02-08) The eq can only be written in one way, left to right, top to bottom, its entry point is the 'float' = ins and outs must balance in less than one unit of time. So we start with defining zero as gatekeeper and how we use f(0) in that position. Remember we must take turns in going through zero as only one direction along a vector passing thru zero is open at a time.

(1-26-08) Proof of Constant. It is literally a physical movement geometric proof. It shows that all Perpendicular pair particles(P+/-) opposite each other on a Moebius surface are exactly the Circumference of the circle apart across the surface. Further no P+/- particles can ever be more than C apart in any direction. Required for a Present to exist in a conserved, yet expanding universe. (?) In fact, a present requires that they always be C apart along some vector across surface. (is this necessary?) Ergo, since C of a circle is known; then any difference form C apart along some vectors = when +/- particles are not perpendicular; then there actual locations are a function of C.

(1-25-08) All fundamental eq. are based upon a constant. e = mcc where c is the constant. I have discovered my constant and now can see all the implications for navigation etc. It is of course an objective characteristic of a +/- pair particle on a Moebius. It is a geometric relationship shared by all particle pairs and shows how the 'present' works and implies the speed between the two sides of surface. We denote our constant C versus c for speed light. With this constant we can tie together the equation using Euler's Identity and some judicious substitutions of Phi/phi and e - mcc and an upside down i for other side of complex plane and now C whioch is tied to Phi/phi.

Plus I have discovered some more properties of a Moebius. i.e take a perpendicular paid particle on a Moebius. put on mid line have them separate in opposite directions and the pair will meet 180 degrees away on mid line. If they could continue they would meet again as a perpendicular pair only each would be on the opposite side from whence they started.

Now send them in same direction and they do not meet but again end up as a perpendicular pair openly each is on the other side from whence they started.

Ergo, an on off switch or a Go/Nogo switch.

(1-20-08)This article gave me the clue for the form of a Moebius eq. When I first realized in early 1991 we lived in a Moebius universe I went down to math dept. at UW to find the eq. for a Moebius in some math book. They did not have such an eq. I was right, it was in a math book somewhere, just not recognized as such.

"From e to eternity" New Scientist 21 July 2007 page 38. In it they discuss "Euler's identity" which is e raised to the power of i times pi + 1 = 0. Here Euler linked together all the fundamental numbers and relationships. 1, of course is Phi/phi, and 0 can be denoted as a function applied to e-mcc = 0. i the imaginary number is only one side of the complex number plane, remember a Moebius has two sides and one surface. pi of course links the circle to a Moebius as the mid line of a Moebius is a circle and its circumference is 2Circumferences of a circle. About transcendental numbers, we need them to navigate on a Moebius.
A note, odd and even are crucial, the longest distance ratio between two possible points on surface of a Moebius going both between two sides and across surface is odd. Same side is even. Since zero is a gate keeper, it 'perceives odd and even', so as to know 'who's turn it is to go through 'origin. Enough for now.

(1-14-08) "A Moebius is trying to minimize the number of perpendicular M/A-M pairpoints.". By perpendicular I mean exactly on opposite sides of the surface. What clinched it was when I asked the question;, "Is there one common objective geometric position all possible M/A-M pairs can take with respect to one another?". Conservation requires a fundamental not do to define its hard boundary with no more.

We can now relate how the the two speeds 'c' and 'between the two sides of surface'(bs) are related. It is almost irresistible to use BS as the symbol for 'between.....', given the way we let ourselves talk to ourselves in public; but lets use lower case(bs). I have high hopes for the future.

An analogous equation is e = mcc where Einstein related the two extreme forms of plus matter in terms of c. Here we have both M and A-M to relate and two speeds. This more fundamental equation links the locations of M and A-M particles on the Moebius's surface by using the two speeds, 'c' and 'bs'.

(1-12-08 i.e. "Where is the center of your coordinate system located with respect to a Moebius?".)

1-10-2008(PM) I figured out the base relationship that the equation describes in a Moebius. It is obvious, a Mr. Ed as soon as you point it out. You can see why a Moebius is trying to bend back on itself once you see this relationship for yourself. The question is, do I show you now?

(1-12-08, the answer) The answer is NO. I don't know who to trust until enough of the right people sign up on the List and our political leaders release their E-T secrets.

(1-14-08) Wrong answer, the answer is YES, science and our situation demand complete public honesty and the banishment of fear. We are one people, one planet and we will live and die together.

The equation is described with this sentence, "A Moebius is trying to ........"(eight words to go including 'the' and 'of').

1-10-2008(AM) Zero is a 'gate keeper'. Only one thing can go through an 'origin' in one direction at a time. Zero remembers this so that when you go across the start end of a 'zero unit' the other end blocks anything else from entering(All vectors or just one and when if more than one?). I will list all the functions that zero has later.

12-20-2007Another article: "Quantum rebel wins over doubters" New Scientist 17 February 2007 page 13. Shariar Afshar(Rowan University at Glassboro, New Jersey. demonstrated that Bohr's complementary principle = 'no experiment can reveal both the wave or particle nature of electrons and protons at the same time' is wrong by showing both at same time. Gorgeous and simple experiment. Gerard 't Hooft likes.

This demonstration is necessary for showing that there is a real 'present' defined by the space between the two sides of a Moebius' surface that connects all of space time into the 'Present' = conserved universe. At the same time it shows that we can not go behind the present = into your own past.

Entanglement is the speed at which a M/A-M maintain there perpendicular =/- relationship despite being separated across the surface.

These particle pairs seek to be close to one another on opposite sides of surface = gravity(?). more on this later.

11-22-2007 These three articles outline the critical points that must be incorporated to create the 'math operation added to e = mcc that will let us describe a Mobeius from where any observer sits on or between its two sides of its surface.

1. "IS THIS THE THEORY OF EVERYTHING" page 8, New Scientist, 17 November 2007. In it Garret Lisi using grant from Foundational Questions Institute maps quantum particles onto an E8 geometry which has a hole all the way through it. Ergo, it is based on a Moebius.

2."THE HYPERTTIME TRAP'
page 36, 13 October 2007, New Scientist. In it Itzhak Bars Univ. of Southern California states that using 2 time dimensions, i.e a plane surface resolves many of Quantum theories problems. We need 2-t to handle moebius strip geometry.

3. "QUANTUM UNENTANGLEMENT' page 36 New Scientist, 3 November 2007 In it Joy Christian of the Univ of Oxford shows that Bell's Theorem is based on wrong assumption = commutative assumption. Rotations are not commutative. By inspection a Moebius is not commutative.

Ergo our relationship uses Clifford algebra, 2-t geometry and 8g geometry.
Enough for now.

4. 12-20-2007Another article: "Quantum rebel wins over doubters" New Scientist17 February 2007 page 13. Shariar Afshar(Rowan University at Glassboro, New Jersey. demonstrated that Bohr's complementary principle = 'no experiment can reveal both the wave or particle nature of electrons and protons at the same time' is wrong by showing both at same time. Gorgeous and simple experiment. Gerard 't Hooft likes.

5. "From e to eternity" New Scientist 21 July 2007 page 38. added 1-20-2008 about Euler's identity and transcendental numbers.

'division by zero' means what? It is actually a position for an operation and we must talk more about what zero does. A zero is not 'nothing' it is a position in coordinate system = origin; a start of an operation, a stop of an operation, a minima, a maxima, a place holder in positional notation, etc.

10-12-2007Zero is both a beginning and an end. Division by zero is the key to the equation. Remember division is repeated subtraction. The real question is how do we get a zero in the denominator, which means the sequence of computational/logical actions that put it there. Once you define it as an x-x, then we can subtract those sequences dependent upon the existence of x from the denominator. My notes have more details and that is enough for now. It is sufficient to say, that in theory we can go anywhere/anytime in the universe that is not behind ourselves in time. So what and how do we define 'behind ourselves in time'. I will update this later.

7-25-07Defining how we use the 'not defined' division by zero position(denominator position) in our calculations is the final component of equation. This is the new mathematical operation that allows us to see whats going on between two sides of Moebius surface. By construction, it tells us which way the surface turns.

I am not going to show this for now. Besides I am still working on the 'symbology'. It will give us the other side of the complex plain.
One thing that is critical is the sequence of operations within a conserved logical system that put the x-x = 0 in the denominator. Further one must clarify the meaning of zero to eliminate the Fallacy of Non-Attribution that mathematicians use when using zero.

8-4-2007: Final comment about mathematicians: When you say "Not Defined" or "Not Permitted", what you unconsciously mean is: "I don't know how to yet.". Not defined, its subjective, can not do that, do not klnow, can not know that, are the signposts of the edge for a scientist looking for new discoveries. Mathematicians are the worst offenders after academics in the use of the 'Fallacy of Non-Attribution". To abstract does not mean you get to throw out your connection ro reality, because by inspection, your symbols are always made from 'reality'. That must always be true or you could not see them.

7-07-07

Once you know what is being conserved by 'living' Moebius strips like us and our universe; then the question is: "How do we tie Phi to our base measure = conserved objective relationship between two fixed physical geometric properties of any Moebius where this relationship always stays same value no matter the changes in the absolute value of these properties?". The answer starts with precisely defining what are we using for the base 'unit' of our always conserved measure = ratio between above two fixed geometric properties. i.e. Phi = 1.62 and phi = .62. Each must be derived from same objective property of base Moebius and thus all subsequent enlargements through dividing will be expressed as fixed predictable multiples of the initial base unit. It is, of course, the diameter of the initial Moebius as all Moebiuses can be defined using a circle. We know how any unit diameter of a circle relates to its circumference = D times pi. How division and expansion of initial unit diameter Moebius occurs has been discussed below and elsewhere.

6-29-07

I have figured out the relationship that is being conserved by our Moebius strip shaped universe. All sensory observations by life forms can be stated using it as the common base unit of comparison between all of our possible scientific observations in our MSS universe. Of course, when its pointed out it is as obvious as the nose on your face. A Mr. Ed. This takes a load off, no navigation in time without it.

6-26-07

Now that I have the coordinate system, the question becomes: What are we conserving? The answer lies on the surface = location and between the two sides of surface. How much faster do we go between the two sides?

6-18-07

Phi/phi ratio is not a division. Its analysis starts from this property: Phi times phi = One. 1.618 times .618 = 1. I have been thinking about how Euclid derived the Extreme to mean ratio, He constructed a pentagon which require five strokes = 5 equal line lengths at proper angles to one another. Draw a five pointed star. So that implies five steps in analysis to derive Phi. e.g. Some ideas; 1. Does drawing Phi using the 1.62 outside circle around Moebius that intersects bowtie perpendicular axis line starting at point on circle below bottom of Moebius that faces bowtie point CREATE a pentagon whose beginning and ending strokes touch the outside edges of bottom of Moebius?

2. When initial 'stroke' starts at bottom of Moebius where bowtie axis hits center of backside then goes to top of bowtie axis at upper edge of Moebius strip; then can we complete a 'pentagon going to three other points on edge of surface that then ends back at start point with last stroke??

6-12-07

How Phi/phi is seen or felt by a Moebius. This is simple but subtle and can only be deduced as it is an 'abstract property' of a Moebius. It is however very real and gives us navigation and incorporates the 'ears of a Moebius'. All Moebii have a centerline which is a circle when you bring two edges together. the Maximum Surface Area (MSA)equation I deduced incorporates phi but we must stand outside of a Moebius to navigate objectively.

The property is this = Theorem: Take a circle of exactly phi unit larger diameter of the Moebius in question = 1.62 diameter of actual Moebius diameter intersecting bowtie line and at a 90 degree angle to Moebius narrow width; then there are only two minimal length line of sight vectors from only two points on the circumference of this larger circle to the end points of any perpendicular pair point between two sides of surface, and ONLY from points on this circle can all points on surface of Moebius be seen. The minimal and maximum pair lengths to both ends of any pair point can be determined apriori.

Ergo, we have navigation. This can be proven that only from this 1.62 diameter 'deduced' circle in space outside a Moebius can all ends of pair points be seen.

In short we have plugged Phi into our universe.

This raises implications for how we are conscious.

5-26-07

How does critical line tell minima that it is where all these 'zeros' are? Answer, It is a float, e.g. like a check float. i.e. When you know when you have 'cash' in on critical date to cover or end float; then what minimal sequence of moves must you take to end the 'float? Look at absolute values in the function and the sequence in which they must occur for minima to be reached.

5-22-07

Riemann Hypothesis, all minima his 'critical line' that is perpendicular to zeta. Yet no one can explain why. i think it is because it is hitting edge of a Moebius surface that is immanent in our symbol structure as we are part of a Moebius universe. Ergo, it is one corner of a Moebius edge. i.e. Edge of Moebius has four corners. so which one is this function showing and will including others explicitly explain the Hypothesis?

5-7-07

I added topic in my forum discussing why topologists were wrong to say Moebius was a one sided surface. I deduced there were four potential sides on observer could see. never more than two at a time. i.e. two from between two sides of surface, and two sides from way outside of Moebius off of its surface. Right on or near outside surface you can only see one side at a time. HMM!! So does off surface imply outside of time??

5-3-07 What relationship is Conserved by EQ

It is the edge width between sides/perpendicular side to side edge width. When two lines between exact opposite edges are drawn, then one will always generate two straight lines at right angles to each other. Further, as the perpendicular opposite edges of circumference approach each other, the ratio is maintained implying edge width decreases in absolute terms. Further, catty corner lines between opposite edges will have predictable angles depending on how far apart in absolute terms the edges are.
(5-05-2007 edit of above plus what follows) these two other non-perpendicular lines imply actual angles of intersection and thus position on surface when used for navigation between the two sides of our single surface.

Once we have a double observing origins whose relationship to each other is defined by the center of the shortest distance separating them, which in turn is the center of the circle that defines the Moebius being described; then we can 'see' how any point on surface or between sides or upon edge relates to all other such points logically with the appropriate term added to e = mcc (the EQ) and the operational relationships implied. (Ergo which end of which unit do we start counting cause and effect from for any particular set of circumstances = where you are at on surface of Moebius.)

4-29-07

Adding a comment on Equation = On coordinate system and how we tie it to a Moebius in a 'conserved equation' form. In short, what is equation conserving through time. e = mcc is a conserved equation but we do not know which way the equation turns; i.e. which way is the past, which way is the future? I know how to do that know. We conserve edge width = constant. Surface area can change = expand. So question, How close can two edges of circumference approach each other? = edge width??? I posit.

Our coor system has two origins(the third the center of circle defining Moebius directly implied). Each gives different vector length to any 'pair point edge width unit' between two sides of surface. Bur edge width is always conserved and it is a ratio of MSA Moebius to circumference. i.e. defined for any circle that defines any Moebius. MORE LATER

4-21-07 On origins for our coor system:

When we count things there is a non explicit assumption used, i.e. which end of our 'unit of measure' do we count. e.g. I start at zero in Cartesian coor system and I go one unit of distance along an axis and I count 1, then one more unit and I count 2; actually you have counted two ends of unit length used. You could just as easily counted starting at zero end and counted two, but then you would only have gone 1 unit distance from origin. Notice a discrepancy comes in when use use negative numbers and we count AD and BC using Christs birthday, e.g. I count backwards from now = 2007 years, starting at which end, either the closest to zero or the farthest, there is a difference of one in the answers = use farthest end and when you reach zero answer = 2008; use closest end to zero = 2007. Notice you have to consciously think about which end to use, from habit and drilling we do so without thinking about the fact that we must use one or the other.

It is this difference I am pointing out. So to use our Moebius coor system and using 'edge width' as base unit (a constant EW/2ddphi = Constant for all Moebii}; then which edge or side of a Moebius we that use matters, e.g. do we use edge that is on side of surface we are measuring on, or opposite surface edge? Hence the note on # below. This note finished 4-21-07

I have reached the point where I have an idea of the 'term' we need to add to e = mcc. It denotes us, we live in the present so this term could be denoted by an = or a #(this symbol is better because our origin has to have four possible starting edges.4-21-07) where we sit between the past and the future in the present. The edges are our familiar two zeros i.e. start and stop; empty or full. When WE, the Is, sit in the present; then where does our objective 'origin' reside with respect to any Moebius; i.e. can we determine the origin of an objective coordinate system for a Moebius?

This origin must sit off of, be outside of, the ideal initial unit Moebius in my assumed empty 3-D Euclidean three space. It must of course like the Bowtie Point be an objective property of our starting ideal half twist Moebius. i.e. You can see it for yourself, yet this ideal point must sit in empty three space, be the one and only unique point that we can use it as the origin for a relatively standard Cartesian coordinate system to see a Moebius from(ourselves from). It allows us to deduce the relationship of any point on a Moebii' surface with any other, or any set of point relationships. Once pointed out, this point of course, must be an "Of Course, its a horse, a talking horse, why its Mr. Ed.". We can literally grab our unit Moebius by its ears from this origin.

Happily, such a point does exist and is a fundamental property of a Moebius, just like the Bowtie Point. I have not figured out what to call it. For now lets call it the Objective Ideal Origin From Which To Observe Moebui. With the knowledge it provides of how to use the Bowtie, we can deduce all aspects of a Moebius with minimal measurements from anywhere upon their surfaces or between their two sides.

Knowledge of how to see this point is ab

Posted by dan1 2005-11-22 03:44:52

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