If a sphere can be tangent to all six edges of a tetrahedron, then the four lines connecting the vertex and the incircle of the opposing triangular face will be intersecting(concurrent) at a point. This point will be different from the center of the sphere.
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| The four circumscribed circles of the four triangles of a tetrahedron will all fall on a sphere, so called circumscribed sphere. |
Reference:
http://en.wikipedia.org/wiki/Circumscribed_circle
These graphs are plotted using Python and its package mplot3D. The programs to generate these figures are pyfig1 and pyfig2.
Got interested in geometry in high school and came up with this project in the science fair.
上面科展中我當時因為一些考量而選擇不加入以下參考書單，因為我所做的確實是我個人做出來的，我是到非常後來才知道這本書，而我不希望當時評審因為我加入了這個清單而有誤會。不過我現在必須說我在後期研究階段確實有參考到下面這本書，尤其在四面體的各個內心外心垂心等等定義上，不過重要的線共點點共線的理論確實是我做的，書上也沒有，我選擇現在補充的原因是因為，在嘗試做出一個我自己的完整的技術文件教材之後，我才了解到出版一本書的困難度，因此我覺得我是需要給出正確參考文獻
- 幾何學辭典，ISBN:957-603-071-4，世部貞市郎原著，九張出版社
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