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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Current time: May 19, 2022, 1:32 am
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A tetrahedron relating the Fibonacci to a pentagon

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Hello and welcome to the forum! (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. Whoopdedoo. 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 onedimensional or twodimensional relation; there is a threedimensional 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 onedimensional or twodimensional relation; there is a threedimensional relation as well And what, precisely, are we to do with this mathematical revelation? Boru
‘Let me never fall into the vulgar mistake of dreaming that I am persecuted whenever I am contradicted.’ Ralph Waldo Emerson
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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 onedimensional or twodimensional relation; there is a threedimensional relation as well Are you alright? 
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