• Remarkable my 238th book of science for AP // Proving the Principle of

    From Archimedes Plutonium@21:1/5 to All on Tue May 2 16:36:04 2023
    Remarkable my 238th book of science for AP // Proving the Principle of Maximum Electricity Production is done by Atoms 44m views
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    238th book of science for AP // Proving the Principle of Maximum Electricity Production is done by Atoms
    44m views

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    Archimedes Plutonium
    Mar 18, 2023, 10:02:09 AM

    So many times I have referred to this principle in my work. Yet I never proved it true. I think it is
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    Archimedes Plutonium
    Mar 18, 2023, 11:21:39 PM

    Alright I need some math data to understand why Maximum Electricity production relates directly to
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    Archimedes Plutonium
    Mar 18, 2023, 11:42:18 PM

    Now looking at the unique features of the Torus. Source StackExchange: The torus is the only surface
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    Archimedes Plutonium
    Mar 19, 2023, 2:38:02 PM

    Now the speed of measured Alpha particles from decay is in the range of 5 to 7 percent the speed of
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    Archimedes Plutonium
    Mar 19, 2023, 11:51:08 PM

    Recently I caught myself writing a trio of books in astronomy, starting with the concept of Stepping
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    Archimedes Plutonium
    Mar 20, 2023, 2:27:00 AM

    Alright, I think I have the proof that the torus is the geometry figure of Maximum Electricity
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    Archimedes Plutonium
    Apr 23, 2023, 2:14:10 PM (8 days ago)

    Alright, onto my 238th book of science. I have often mentioned this principle in my physics work.
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    Archimedes Plutonium
    Apr 23, 2023, 5:06:17 PM (8 days ago)

    I suspect the Maximum Electricity Principle is the reverse of Least Action or Least Energy principle,
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    Archimedes Plutonium
    Apr 27, 2023, 11:27:21 PM (4 days ago)

    I need a full book on Maximum Electricity Production Principle in order to say the S, P, D, F
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    Archimedes Plutonium
    Apr 28, 2023, 9:24:25 AM (3 days ago)

    I am going to try for 2 different methods of proof of Maximum Electricity Production. One method is
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    Archimedes Plutonium
    Apr 28, 2023, 12:06:03 PM (3 days ago)

    On Friday, April 28, 2023 at 9:23:19 AM UTC-5, Archimedes Plutonium wrote: > I am going to try for
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    Archimedes Plutonium
    Apr 28, 2023, 9:32:30 PM (3 days ago)

    Alright, I am not going to have any problems with figuring out the geometry inside of Atoms, for I
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    Archimedes Plutonium
    Apr 28, 2023, 11:20:05 PM (3 days ago)

    On Friday, April 28, 2023 at 9:30:14 PM UTC-5, Archimedes Plutonium wrote: > Alright, I am not
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    Archimedes Plutonium
    Apr 29, 2023, 5:57:07 AM (3 days ago)

    On Friday, April 28, 2023 at 11:19:34 PM UTC-5, Archimedes Plutonium wrote: > On Friday, April 28,
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    Archimedes Plutonium
    Apr 29, 2023, 4:09:32 PM (2 days ago)

    Now this total overhaul of the geometry of the interior of all Atoms is going to make me say that the
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    Archimedes Plutonium
    Apr 29, 2023, 11:57:22 PM (2 days ago)

    On Saturday, April 29, 2023 at 5:56:34 AM UTC-5, Archimedes Plutonium wrote: > Copper is 1s-2, 2s-
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    Archimedes Plutonium
    Apr 30, 2023, 1:14:04 AM (2 days ago)

    Now here I have to stop for a moment and worry and wonder of a factor in efficiency. The worry is
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    Archimedes Plutonium
    Apr 30, 2023, 8:54:33 AM (yesterday)

    So I ask the question again is there a mathematics easy way of computing that 50 for copper, rather
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    Archimedes Plutonium
    Apr 30, 2023, 3:25:25 PM (yesterday)

    So I am intrigued here because I am making the case that photons and neutrinos from dipoles. That a
    Message has been deleted
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    Archimedes Plutonium
    Apr 30, 2023, 8:20:27 PM (yesterday)

    Alright this leads directly into the idea that the composition of the Proton as a 840MeV torus and
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    Archimedes Plutonium
    Apr 30, 2023, 11:33:15 PM (yesterday)

    On Sunday, April 30, 2023 at 8:16:55 PM UTC-5, Archimedes Plutonium wrote: > Alright this leads
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    Archimedes Plutonium
    May 1, 2023, 7:39:22 AM (yesterday)

    Alright, this is becoming extremely interesting. I have the world divided between either a Transverse
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    Archimedes Plutonium
    May 1, 2023, 1:07:26 PM (19 hours ago)

    I am looking on how to recover a Semicircle wave in the manner that a cycloid wave is constructed.
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    Archimedes Plutonium
    May 1, 2023, 1:48:32 PM (18 hours ago)

    Alright, some good signs in all of this mess. I am looking for rolling of closed curves that recovers
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    Archimedes Plutonium
    May 1, 2023, 2:00:38 PM (18 hours ago)

    Now looking at the Limacon, if we stipulate that the offcenter point has to always be as a
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    Archimedes Plutonium
    May 1, 2023, 7:28:19 PM (12 hours ago)

    On Monday, May 1, 2023 at 1:02:23 PM UTC-5, Archimedes Plutonium wrote: > I am looking on how to
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    Archimedes Plutonium
    May 1, 2023, 9:53:05 PM (10 hours ago)

    So, well, Wikipedia has a animation of a Limacon and the Convex Limacon is almost a circle but a part
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    Archimedes Plutonium
    May 1, 2023, 10:57:40 PM (9 hours ago)

    Now I am going to go contrary to the description of the Dimpled Limacon and say that the Pointer-
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    May 1, 2023, 11:23:28 PM (8 hours ago)

    Now I am pretty sure this is a flaw in Old Math Geometry of their Limacon pointer marker going around
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    On Monday, May 1, 2023 at 11:23:28 PM UTC-5 Archimedes Plutonium wrote:
    Now I am pretty sure this is a flaw in Old Math Geometry of their Limacon pointer marker going around like a clock as the motion of the moving circle goes around. The AP Limacon is where the pointer marker needs to stay perpendicular to the tangent of
    the stationary circle, thus creating a new larger circle with one intersection point. I say this because there is no other mechanical means of producing concentric circles or intersection at one point of two circles.

    It is understandable that people would be interested in the 2-motions of Old Math Limacon, the motion of rolling one circle over another circle, but also the motion of the Pointer-Marker, for the Limacon of Old Math is obfuscating but yields figures for
    Art and Artwork, but not figures for Physics of electricity and magnetism.

    In Physics we are more precise than goonclods of Old Math with their double motions. In New Math we have only one motion, the rolling of one circle over another. Or the rolling of 1 ellipse over another and producing a new circle-- once the mess up of
    the motion of the pointer-marker is corrected.

    In New Math, in rolling figures we allow only one motion. And we Well-Define the Pointer Marker as not having motion and has a Infinitesimal length of at least 1*10^-604 distance length. And this Pointer Marker must be perpendicular at all times to the
    rolled-over tangent of stationary figure. So in the MathStackExchange figure of ellipse rolling over identical ellipse, it actually is a Circle once the Pointer Marker mistakes are corrected.

    Now it took me all of just 2 minutes today to get a sheet of tracing paper and trace out the cycloid on page 293 of Jacobs "Mathematics: A Human Endeavor". And then roll my second cycloid over the perimeter of Jacobs cycloid. Using the pointed tip (not
    the center of second cycloid but the pointed tip as Pointer-Marker. Now keeping the pointed tip always with its length as a perpendicular to the tangent of the stationary cycloid what that rolling traces out is indeed a Semicircle.

    So here we can start some Conjectures:

    Conjecture 1, rolling a ellipse over a identical ellipse, keeping pointer-marker perpendicular produces a circle.

    Conjecture 2, rolling a circle over another circle keeping pointer-marker perpendicular produces a circle.

    Conjecture 3, rolling a cycloid over identical cycloid, keeping pointer-marker perpendicular produces a semicircle.



    Physics needs the **perpendicular** for the pointer-marker, for electricity is always perpendicular to magnetism.

    The Old Math Geometry Limacon is actually 2 rollings, the rolling of one circle over another and the independent rolling of a pointer marker. In the AP Limacon, there is but one rolling the circle over the other circle, while the pointer-marker is a
    fixed perpendicular point.


    Old Math Geometry of its roulette math and Limacon are ill-defined in their pointer-marker and theirs is mostly math for Art work, not physics electricity and magnetism.



    This messy obfuscation of what is moving also can solve the two identical ellipses rolling one over the other as tracing out a perfect circle. It is almost producing a perfect circle in the MathStackExchange animation but slightly off. And I am saying it
    is only slightly off because the animation was not programmed to allow the pointer marker, the center of the rolling ellipse to always have a perpendicular to the tangent of the stationary ellipse. You see the programmers of that animation, are like the
    Limacon animation and not restricting the pointer-marker to be always a perpendicular, and that is the reason it is not a perfect circle. This means having the pointer marker be a tiny tiny length, the infinitesimal of mathematics, a length of 1*10^-604,
    a small positive number and length that needs to stay perpendicular to stationary figure surface tangent.

    Now I need to do the same thing with the cycloid, see if I can roll one cycloid over a stationary cycloid with a pointer-marker and see if I trace out a semicircle. I may have to use the midpoint of the line segment that connects the two ends of one
    cycloid wavelength.


    Wrong I need just the pointed tip ends, either one will do as a pointer-marker. By tip end I am speaking of the letter C if that were a cycloid seen sideways, has two tip ends.


    Yes, in geometry if you are not in the habit of first doing a problem with hand cut outs and seeing for yourself the outcome, then you are not doing geometry correctly. Those that think they can apply algebra without seeing a hand on demonstration are
    doing just kook math geometry.

    AP, King of Science, especially physics and logic
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    3:09 PM (3 hours ago)



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    Alright, good on MathStackExchange for they have something on cycloid rolling. Titled "Cycloid rolls on another identical Cycloid" 6years-4months ago. They have a animation and the figure it traces is looking like half a stadium geometry shape. However,
    they use as Point-Marker the center of the straightline segment of the cycloid. And I suspect they do not keep their point-marker always at a perpendicular to the surface of stationary cycloid. If they keep their point-marker perpendicular to tangent of
    surface, I suspect it becomes a semi-ellipse rather than half a stadium.

    What AP uses as Point-Marker is either one of the corners and keeping this point-marker perpendicular, I trace out a Semicircle.

    AP
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    5:56 PM (1 hour ago)



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    Major, major Geometry in Motion discovery by Archimedes Plutonium. I discovered this in this writing of 238th book. The discovery I made is that the cycloid Wave is an Ellipse wave. The error of Old Math Geometry is that they had 2 motions in a rolling
    circle on the straightline. They had the motion of the circle which is wanted, but they also had a 360 degree motion of the Pointer-Marker on the surface of the rolling circle. What this causes is the end product of a cycloid with 2 vertices if we put
    half and half together.

    When we stipulate only one motion and not two motions, and when we stipulate the Point-marker is always perpendicular to the surface of straightline, that the Point-Marker is actually a infinitesimal distance length that is constantly perpendicular to
    the straightline, that the final curve is a ellipse and has no vertices.

    A cycloid with vertices is actually a fiction geometry produced by a circle in motion.

    This chimes back to one of my conjectures a long time ago, that the only smooth curve produced by circle rolling is either ellipses or circles. There is a quantization of smooth curves as produced by conic sections and so the Old Math Geometry of Motion
    Geometry erred in motion by a ill-defined notion of the Point-Marker, and that this Point-Marker is ill-defined in Old Math and it has a silly stupid motion itself.

    This is a huge major discovery for Geometry in Motion for it directly impacts Physics electromagnetism.

    The cycloid curve of Old Math is a error filled fictional curve. Much like the slant cut of right-circular cone is a Oval, never the ellipse, and the oval broadly defined is the adding of two different ellipses to form a oval. Still within the AP
    conjecture-- the only smooth curves in geometry (have no vertices) are New Math conic sections.

    This deserves a separate math book for it is a huge major change in Geometry of Motion.

    AP
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    6:16 PM (18 minutes ago)



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    Now I have a easy intuitive proof that I am correct the cycloid is actually a ellipse. Some geometers call this a synthetic proof where we argue a simple insight. In this case we focus upon the midpoint of the cycloid wave-- 1 cusp. This midpoint is
    rather flat and it is flat because the Pointer-Marker is parallel to the straightline it is rolling upon. That means the points on both sides of the midpoint are also parallel and thus a straightline ridge. Now for AP's Pointer Marker that is always
    perpendicular to straightline causes the midpoint ridge of cyloid to be higher than the points to the right and left of the midpoint ridge. This is the description of the ellipse. While the cycloid with its flat ridge actually is not a smooth curve at
    the ridge but contains vertices as it transits from straight line ridge to being a curve again. This constitutes a Proof that Cycloids are actually Ellipses. And also I need to show that at the ends of the cycloid cusp that those angles are different in
    the AP cycloid than the ill-defined Old Math cycloid.

    This is again, a huge major discovery, not so much for Mathematics which used this stuff for Art and Art Work, but for Quantum Electrodynamics, for EM of physics is all about Particle and Wave, and the cycloid is the particle of the rolling circle upon
    the straightline which is the wave of Physics. The Faraday law of a Torus being the Proton is all about geometry of smooth curves. And geometry is basic and fundamental to physics.

    On Tuesday, May 2, 2023 at 5:59:55 PM UTC-5 Archimedes Plutonium wrote: Major, major Geometry in Motion discovery by Archimedes Plutonium. I discovered this in this writing of 238th book. The discovery I made is that the cycloid Wave is an Ellipse wave. The error of Old Math Geometry is that they had 2 motions in a rolling
    circle on the straightline. They had the motion of the circle which is wanted, but they also had a 360 degree motion of the Pointer-Marker on the surface of the rolling circle. What this causes is the end product of a cycloid with 2 vertices if we put
    half and half together.

    When we stipulate only one motion and not two motions, and when we stipulate the Point-marker is always perpendicular to the surface of straightline, that the Point-Marker is actually a infinitesimal distance length that is constantly perpendicular to
    the straightline, that the final curve is a ellipse and has no vertices.

    A cycloid with vertices is actually a fiction geometry produced by a circle with two motions.

    This chimes back to one of my conjectures a long time ago, that the only smooth curves produced by circle rolling is either ellipses or circles or New Math conic sections. There is a quantization of smooth curves as produced by conic sections and so the
    Old Math Geometry of Motion Geometry erred in motion by a ill-defined notion of the Point-Marker, and that this Point-Marker is ill-defined in Old Math and it has a silly stupid motion itself.

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  • From Archimedes Plutonium@21:1/5 to All on Tue May 2 17:56:43 2023
    This makes sense that circle rolled on straightline is ellipse. Ellipse rolled on identical ellipse makes circle. But it leaves out what happens when circle is rolled on ellipse or ellipse rolled on circle all of which the Pointer-Marker is kept
    perpendicular to rolled surface.

    AP

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  • From Archimedes Plutonium@21:1/5 to All on Tue May 2 19:55:49 2023
    Archimedes Plutonium<plutonium.archimedes@gmail.com>
    5:59 PM (4 hours ago)



    to Plutonium Atom Universe
    Major, major Geometry in Motion discovery by Archimedes Plutonium. I discovered this in this writing of 238th book. The discovery I made is that the cycloid Wave is an Ellipse wave. The error of Old Math Geometry is that they had 2 motions in a rolling
    circle on the straightline. They had the motion of the circle which is wanted, but they also had a 360 degree motion of the Pointer-Marker on the surface of the rolling circle. What this causes is the end product of a cycloid with 2 vertices if we put
    half and half together.

    When we stipulate only one motion and not two motions, and when we stipulate the Point-marker is always perpendicular to the surface of straightline, that the Point-Marker is actually a infinitesimal distance length that is constantly perpendicular to
    the straightline, that the final curve is a ellipse and has no vertices.

    A cycloid with vertices is actually a fiction geometry produced by a circle with two motions.

    This chimes back to one of my conjectures a long time ago, that the only smooth curves produced by circle rolling is either ellipses or circles or New Math conic sections. There is a quantization of smooth curves as produced by conic sections and so the
    Old Math Geometry of Motion Geometry erred in motion by a ill-defined notion of the Point-Marker, and that this Point-Marker is ill-defined in Old Math and it has a silly stupid motion itself.

    This is a huge major discovery for Geometry in Motion for it directly impacts Physics electromagnetism.

    The cycloid curve of Old Math is a error filled fictional curve. Much like the slant cut of right-circular cone is a Oval, never the ellipse, and the oval broadly defined is the adding of two different ellipses to form a oval. Still within the AP
    conjecture-- the only smooth curves in geometry (have no vertices) are New Math conic sections.

    This deserves a separate math book for it is a huge major change in Geometry of Motion.

    AP
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    6:15 PM (4 hours ago)



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    Now I have a easy intuitive proof that I am correct the cycloid is actually a ellipse. Some geometers call this a synthetic proof where we argue a simple insight. In this case we focus upon the midpoint of the cycloid wave-- 1 cusp. This midpoint is
    rather flat and it is flat because the Pointer-Marker is parallel to the straightline it is rolling upon. That means the points on both sides of the midpoint are also parallel and thus a straightline ridge. Now for AP's Pointer Marker that is always
    perpendicular to straightline causes the midpoint ridge of cyloid to be higher than the points to the right and left of the midpoint ridge. This is the description of the ellipse. While the cycloid with its flat ridge actually is not a smooth curve at
    the ridge but contains vertices as it transits from straight line ridge to being a curve again. This constitutes a Proof that Cycloids are actually Ellipses. And also I need to show that at the ends of the cycloid cusp that those angles are different in
    the AP cycloid than the ill-defined Old Math cycloid.

    This is again, a huge major discovery, not so much for Mathematics which used this stuff for Art and Art Work, but for Quantum Electrodynamics, for EM of physics is all about Particle and Wave, and the cycloid is the particle of the rolling circle upon
    the straightline which is the wave of Physics. The Faraday law of a Torus being the Proton is all about geometry of smooth curves. And geometry is basic and fundamental to physics.

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    This makes sense that circle rolled on straightline is ellipse. Ellipse rolled on identical ellipse makes circle. But it leaves out what happens when circle is rolled on ellipse or ellipse rolled on circle all of which the Pointer-Marker is kept
    perpendicular to rolled surface.

    In the Limacon's of circle rolled over another circle produces circles when the Pointer Marker is kept perpendicular.

    So what is a ellipse rolled over a circle? I hazard to guess another ellipse. And for circle rolled over ellipse, I guess another ellipse. What about two different sized ellipses? Here the problem is going to be if there is a fractional rolling? By
    fractional I mean both do not come to a smooth finish of 360 degrees and have left-over arc-length. In those cases I would say look and examine the curve to see if it is going to be a circle or becoming a ellipse.

    AP
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    This deserves a new separate math book on the massive corrections and changes to Geometry in Motion. The rolling requires only 1 motion as a category of figures. If we have two items in motion such as the circle then the Marker-Point in motion also, then
    different geometry figures result.

    But also, I need to well-define the concept of Smooth Curve in New Math. Old Math was pathetic on this issue also.

    So I have the Conjecture that all and only smooth curves in mathematics can all be got from cone, and cylinder cuts. Anything that is not a cone and cylinder cut is not a Smooth Curve.

    And let me get on what that Well-Defined Smooth Curve is. I speculate that the well defined smooth curve in discrete math since all of math geometry is discrete with its Decimal Grid Number System-- there exists empty space between any two given numbers
    in mathematics. So a well defined smooth curve, each point and its successor point and predecessor point is related by the number constant of pi=3.14159.... If a point is not related to the next point on a curve (discrete geometry) by 3.1415... then the
    curve is __not smooth___ and we call that point a vertex.

    In line geometry we had no trouble in defining a vertex as where a angle that is not 180 degrees from one point to the next occurs.

    But in curve geometry of Old Math, they never well-defined a vertex on a curve. I define it as a breakdown in pi = 3.14..... of a point and its successor point.

    AP

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  • From Archimedes Plutonium@21:1/5 to All on Thu May 4 09:57:50 2023
    Alright, I am onto a project I love doing, totally absorbed. So I get out my geometry wood blocks and craft toruses.

    The first torus comes from a 3 by 3 by 3 cube of wood blocks. There are 27 such blocks for volume of this 3by3by3 cube. We call that a 27 cubic Cube.

    Now I remove the inner column of 3 blocks to make a torus geometry. As I remove that inner column I am now left with a torus of volume 27-3 = 24 cubic torus.

    Now the Surface Area S.A. of 3by3by3 original cube of volume 27 cubic blocks is that of squares. The original cube has a face side of 3x3 = 9 square and there are 6 such faces so there is 9x6= 54 square area.

    Now compare Volume to S.A. is 27/54 and volume is 1/2 of S.A. or S.A. is 2 times volume.

    The S.A. of the torus 3by3by3 is upon removal of inner 3, the S.A. is 4 faces of 9 gives 4x9 = 36, with 2 faces of 8 is 2x8= 16, and then the faces for the donut hole are 12. Adding up those squares gives 36+16+12 = 64.

    So, for this torus its volume is 24 and its Surface Area is 64 for a ratio of 24/64 = 0.375 or 2.66...

    Now I do the very same accounting of the 4 by 4 by 4 cube with a donut hole of removal of inner 2by2by4.

    What I am focusing in upon is that Maximum Electricity comes from a tokamak or torus geometry because of surface area so much larger than volume.

    AP

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  • From Archimedes Plutonium@21:1/5 to All on Thu May 4 15:34:35 2023
    Alright, working on the 4 by 4 by 4 torus of wood blocks. So the 4 by 4 by 4 Cube is volume of 64 cubic volume and its Surface Area S.A is 16 squares for each 6 faces. That is a S.A. of 16 x 6 = 96 square S.A.

    Now I remove 2 by 2 by 4 blocks in the center of 4 by 4 by 4 Cube to form a Torus. Thus the volume of this 4 by 4 by 4 torus is 64 - 16 = 48 cubic Volume of torus. the surface area of torus of 4 by 4 by 4 is going to be after removing 16 inner blocks is
    going to be 4 faces of 16, 2 faces of 12 squares and the donut hole inner faces are 8 x 4. So adding these squares I have (4x16) + (2x12) + (4x8) = 64+24+32 = 120 square surface area.

    Summary of ratios:

    For 4 by 4 by 4 Cube has volume 64 and S.A of 96, for a ratio of 64/96 or of 96/64. These ratios are 0.6666... and 1.5.

    Now comparing the 3 by 3 by 3 torus ratio with 4 by 4 by 4 torus. The 3 by 3 by 3 torus ratios are 24/64 or 64/24 which is 0.375 and 2.66...

    For the 4 by 4 by 4 Torus has volume of 48 and S.A. of 120. This ratio is either 48/120 or 120/48 yielding 0.4 and 2.5.

    Let me spend some time to see if I made a arithmetic error.

    AP

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  • From Archimedes Plutonium@21:1/5 to Archimedes Plutonium on Thu May 4 18:33:30 2023
    On Thursday, May 4, 2023 at 5:34:39 PM UTC-5, Archimedes Plutonium wrote:
    Alright, working on the 4 by 4 by 4 torus of wood blocks. So the 4 by 4 by 4 Cube is volume of 64 cubic volume and its Surface Area S.A is 16 squares for each 6 faces. That is a S.A. of 16 x 6 = 96 square S.A.

    Now I remove 2 by 2 by 4 blocks in the center of 4 by 4 by 4 Cube to form a Torus. Thus the volume of this 4 by 4 by 4 torus is 64 - 16 = 48 cubic Volume of torus. the surface area of torus of 4 by 4 by 4 is going to be after removing 16 inner blocks
    is going to be 4 faces of 16, 2 faces of 12 squares and the donut hole inner faces are 8 x 4. So adding these squares I have (4x16) + (2x12) + (4x8) = 64+24+32 = 120 square surface area.

    Summary of ratios:

    For 4 by 4 by 4 Cube has volume 64 and S.A of 96, for a ratio of 64/96 or of 96/64. These ratios are 0.6666... and 1.5.

    I had better use one ratio the ratio of Surface Area / volume, so for the 4 by 4 by 4 Cube I have 96/64 = 1.5.


    Now comparing the 3 by 3 by 3 torus ratio with 4 by 4 by 4 torus. The 3 by 3 by 3 torus ratios are 24/64 or 64/24 which is 0.375 and 2.66...


    The 3 by 3 by 3 torus ratio is 64/24 = 2.66. The 4 by 4 by 4 torus ratio is 120/48 = 2.5. Which has me suspicious of a arithmetic error.

    For the 4 by 4 by 4 Torus has volume of 48 and S.A. of 120. This ratio is either 48/120 or 120/48 yielding 0.4 and 2.5.

    Let me spend some time to see if I made a arithmetic error.

    AP

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  • From Archimedes Plutonium@21:1/5 to All on Thu May 4 19:52:24 2023
    The 5 by 5 by 5 Cube.
    Volume = 125
    S.A. = 6 x 25 = 150

    5 by 5 by 5 torus (by removing 3 by 3 by 5 blocks in center)
    Volume = 125 - 45 = 80
    S.A. = (4x25) + (2x16) + (3x3x5) = 100 +32 + 45 = 177

    Ratio 177/80 = 2.212....

    So I have a sliding down convergence of a sequence. The 3x3x3 torus was 2.666.... the 4x4x4 torus was 2.5 and the 5x5x5 is 2.212....

    So what is the point of convergency at Infinity which is a 1*10^604 Cube? If I had to guess, I would guess the convergency is 1.61.....

    AP

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