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: June 6, 2020, 9:50 am
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A tetrahedron relating the Fibonacci to a pentagon

At work.
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
'A man is accepted into a church for what he believes. He is turned out for what he knows.'  Mark Twain
I feel geometrically violated.
(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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Welcome! You will have to put money into my paypal account to get me to play math with you!
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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
'A man is accepted into a church for what he believes. He is turned out for what he knows.'  Mark Twain
A weird email as username... I never knew there was an atheist.com domain
(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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