If you take a regular tetrahedron and keep the angles at one vertex unchanged but change the lengths from the vertex to any three successive terms of the Fibonacci series you will find the new fourth face to have one side of a pentagon and the two internal diagonals.
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A tetrahedron relating the Fibonacci to a pentagon
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At work.
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 (July 7, 2019 at 8:47 pm)[email protected] Wrote: If you take a regular tetrahedron and keep the angles at one vertex unchanged but change the lengths from the vertex to any three successive terms of the Fibonacci series you will find the new fourth face to have one side of a pentagon and the two internal diagonals. Well, THAT'S a relief. I've spent years taking irregular octahedrons, changing all the angles of the all the vertices, bisecting along the interior acutrix of the nebulonic series, and getting a thundering headache as a result. Boru
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 (July 7, 2019 at 8:47 pm)[email protected] Wrote: If you take a regular tetrahedron and keep the angles at one vertex unchanged but change the lengths from the vertex to any three successive terms of the Fibonacci series you will find the new fourth face to have one side of a pentagon and the two internal diagonals. Drawings or it didn't happen. And, if I understand what you have posted, you have a triangle. Whoop-de-doo. Triangles are a dime a dozen.
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well I dont know how to upload drawings but you can prove this yourself with just the sine and cosine laws...anyway all I'm saying is the Fibonacci series doesnt just have a one-dimensional or two-dimensional relation; there is a three-dimensional relation as well
(July 8, 2019 at 5:44 am)[email protected] Wrote: well I dont know how to upload drawings but you can prove this yourself with just the sine and cosine laws...anyway all I'm saying is the Fibonacci series doesnt just have a one-dimensional or two-dimensional relation; there is a three-dimensional relation as well And what, precisely, are we to do with this mathematical revelation? Boru
‘I can’t be having with this.’ - Esmeralda Weatherwax
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 (July 8, 2019 at 5:44 am)[email protected] Wrote: well I dont know how to upload drawings but you can prove this yourself with just the sine and cosine laws...anyway all I'm saying is the Fibonacci series doesnt just have a one-dimensional or two-dimensional relation; there is a three-dimensional relation as well Are you alright? |
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