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Current time: October 16, 2019, 8:27 pm

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A tetrahedron relating the Fibonacci to a pentagon
#1
A tetrahedron relating the Fibonacci to a pentagon
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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#2
RE: A tetrahedron relating the Fibonacci to a pentagon
At work.

Hello and welcome to the forum! Big Grin
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#3
RE: A tetrahedron relating the Fibonacci to a pentagon
(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
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#4
RE: A tetrahedron relating the Fibonacci to a pentagon
I feel geometrically violated.
God(s) and religions are man made and the bane of humanity. 

Of all the things I've lost, I miss my mind the most. Ozzy or Twain/take your pick
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#5
RE: A tetrahedron relating the Fibonacci to a pentagon
(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.
I never thought I'd live long enough to become a grumpy old bastard. Here I am, killing it!
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#6
RE: A tetrahedron relating the Fibonacci to a pentagon
Welcome! You will have to put money into my paypal account to get me to play math with you!
"It is my firm belief that it is a mistake to hold firm beliefs" - From the Principia Discordia







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#7
RE: A tetrahedron relating the Fibonacci to a pentagon
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
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#8
RE: A tetrahedron relating the Fibonacci to a pentagon
(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
'A man is accepted into a church for what he believes.  He is turned out for what he knows.' - Mark Twain
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#9
RE: A tetrahedron relating the Fibonacci to a pentagon
A weird e-mail as username... I never knew there was an atheist.com domain Dodgy
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#10
RE: A tetrahedron relating the Fibonacci to a pentagon
(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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