If Mr. Too Stoned is to attack my claim this is the process he should take:
1- Ascertain if or not I have arrived at a method of finding that angle. I have.
2- There might then be an argument, given the degrees in a circle, that I have just randomly hit on some constructs of lines, circles and points that seem to get the same angle. I can counter that with ease, but it is at least an argument.
3- Mr. Too Stoned next step would be to see if it can be proved another way. It was. With radians. I have that work, it was done by another.
.Gee this proof has little symbols. Mr. Donovan’s proof has lines and points. Complete switch of systems. With that stupidity Mr. Too Stoned follows by simple name calling
Here we go:
Set the ruler to pixels. Make a hairline 6000 pixels high. This measurement and one sixth of it, 1000 pixels, are the critical measurements. I am assuming you are zooming and getting exact. Place this 6000 pixel line on a zero guideline. (be exact). Construct two angled guidelines, one of 60 and one of 120 degrees. Have them intersect with the top of the 6000 pixel line. Be exact. If the line is set at 'hairline' as it should be the width should still be almost a pixel. So have the lines cross in the middle. There is some zooming in and out quite a bit at the start. The 60 and 120 degree lines should now make an equilateral triangle. Use bezier tool and 'snap to guidelines' to make that shape. REMEMBER the lines are in the center of these guidelines. We will be measuring angles from the top of this triangle. You might make a crosshair very small at top. Something to show you that the very top of the shape is not the top, see where the centers of the lines meet. Now you need make a circle close to what the triangle would fit into if tip and center and two sides touching the circle. This does not need to be as exact. Get it close as you can. You can spend extra time getting it very exact but it will not buy you much. However, when placing over so that the top of triangle is in center and two bottom corners touch the circle, make sure the left side of the parts that touch the circle, (bottom left), is exact. Remembering again that the real center of the line is inside the approx. 3/4 of a pixel thick line understand that the sharp corner of the triangle will stick out a bit from the circle.
'Group' the work above or set in a layer so it does not come apart.
Now one more exact measure. This is 1/ 6th of the original 6000 pixel line. But we make it with a circle, showing various angles with this, so make a circle with an exact 2000 pixel diameter, and you may even want to put small crossshairs in the center. 'Group' this. Move this smaller circle, green in the diagram so that it sits direct on the center of where triangle crosses the greater circle. And when exact, group the entire thing. All the exact work is now done. So you have ballpark understanding, set, one at a time, four lines through the top of the pyramid. First do the 51.84444~ which I did in red. In yellow I did the parameters for understanding, I set one at 52 exact degrees and another at 52 exact degrees and did this in yellow. Also a darker yellow 52.73 degrees. Notice how the circle (smaller circle) cuts twice through the red, but about 51.73 at the greater circle.
Now for explanation:
1- As the six pyramids begin to move into, "eat up" the eight tetrahedrons, how for does each face of the pyramid move. It does not move to the center because there are five other moving as well. Each face need only move at 1/6th, the measurement of the radius of the lessor circle. The big triangle is the shape of the face of the six pyramids. It is also the shape of the base of the tetra exactly. So every face of each of the six pyramids moves from on side toward a tip. So the distance it moves is across, not one of the sides.
2- Notice that if it is considered that the base is the first move here, it is about 51.73.
3- However, we have the distance the face will move, 1000 pixels, but not the exact direction. As the pyramids are 'filling' up the tetras are decreasing. Therefore the angle that the bottom of the face moves is to be considered. The greater arc is the obvious limit. As they are all moving the other limit is half the 6000., 3000. Place lines of 3000 and 6000 so that they go from the corner of the pyramid to the arc. (I don't think the bottom blue line of 3000 comes through. However this angle is bisected which is the angle of second blue line. And you can see where that intersects the 51.84444~ given. Understand that the 51.844444, given by Taylor first is a formula based and theoretical. A visual of this concept has not yet been given except here.
Anyone who does this with a construction of 13 ping pong balls in hand will feel it as well as understand it.
This visual came up as I was working on my book Message Of The Crop Circles. A great portion of the crop circles point to this new geometry. The book is about 70 percent complete with many illustrations. I do not as yet have a publisher.
Figure ABCDEF as drawn below
Figure ABCDEF is not a polygon.
We are given figure ABCDEF which is a union of segments in a plane. connects only to at point B, and point A is left unintersected. also connects to at C. also connects to at D. connects to at E. connects to no other segment and in fact, point F is left completely unintersected. Now since figure ABCDEF has two segments, and , which only connect with one other segment, it cannot be a polygon. For in a polygon, by definition, all segments intersect two others, one at each endpoint.
Go to the diagram, use the steps, see what angle you come up with.
Then go back and see if you can argue
Translation: Using my rules, disprove me.
Sorry, I don't have CAD. But even if I did I know carny come on when I hear one, and if I use your balls and your bottles it won't matter how hard I hit them they won't fall 'cause they're all glued together with a major layer of crap.
I challenge you to use the well known and widely accepted rules and protocols of mathematical notation and write a "geometry proof" to back up your assertions. Preferably in 2-column form but a "paragraph proof" will work just fine.
So far nothing you have presented fits into the math definition of "proof, so if you can't write it as a "proof" don't claim it is a "mathematical proof"
http://www.themathlab.com/geometry/mathcourt/writeproofs.htmThe two most important things a proof must possess are clarity and backup.
Over the years, we've read some awful proofs and some wonderful proofs. Without a doubt the wonderful ones were wonderful because WE COULD UNDERSTAND THEM!!!!!
There is absolutely no reason to write a proof unless your reader can understand what you're saying. Keep this in mind as you write. We always try to pretend we are speaking to someone who has very limited mathematical knowledge and who doesn't know what facts we have been "given".
So don't worry about trying to match a "perfect wording". Just be sure that your statements are clear, and that they are each backed up with a legal reason.
A good measure of the quality of your proof is found by reading it to a person who has not taken a geometry course or who hasn't been in one for a long time. If they can understand your proof by just reading it, and they don't need any verbal explanation from you, then you have a good proof.
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