The tetrahedron is
Ta = a*(a+1)*(a+2)/6 ; where 'a' is an integer.
Lemma :
A tetrahedron may be the sum of two tetrahedrons*
Peculiar! A cube is never a sum of two cubes, according to FLT. Seems I don't know the properties of the integers. Do I understand Pythagoras' theorem? Probably not.
This is one relation between the tetrahedron and the cube. There are others, but I have difficulties drawing them. Some other day, maybe.
Today I discovered the OpenOffice programs from Sun. They're free, and contain a lot of facilities. I feel an easy-to-understand proof should be graphical. I do not want to create optical illusions, since I am most serious right now.
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* I have a beautiful proof for this lemma, but I don't want to write it right now.
5 comments:
Just passing by to say Hi and how are you?
Hi! I am fine. How are you? Do you take interest in climbing? I have heard Britain is full of nice mountains. Dover
Tnx for climbing in my comment box :-)
And I thank you. This was a VI+. I tried to find the crucial point, but I failed. I must admit I have prejudice about you. This is a disadvantage. I thought you had heard someting on the radio (I listned to the same program), and you were blogging on that theme. The blog was more complex, which I discovered after having laid my comment. If I were not disabled, I would invite you for a walk in the forest. I think we have a lot in common. If one can't talk while strolling in the woods, one can at least discuss things in this media. Not superficial and not too deep, since I have too little knowledge and too many prejudies.
I wish you a stimulating weekend.
/NB
Can't imagine, why nobody comments the blog. When I wrote about Reich, I got a comment related to the blog text, but the comment was anonymous. Can someone explain to me, why a cube (integer) can't be divided in two cubes, while a tetrahedron can.
A close-packed cube cell contains 14 points, the simple 8 and bodycentered 9. What is the structure of the "real number cube"? Is there a structure? I am stuck here. I will have to simplify.
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