Breakfast at Blue Pumpkin
So it's Wednesday and I am here in Pnom Penh. It's really nice outside today. I am looking at some of the problems in the wonderful book by Prof. Steinhauss.
The first problem was about a variation of Pythagoras theorem x^n+y^n=z^n we had to prove that of n>z then no solution is possible.
The other nice problem was about given 4 random points (non collinear) a, b, c and d and it was asked to prove that if it is always possible to draw circle which can contain the 4th vertex inside the circle. We should recall that if there are 3 non collinear points they always define a unique circle.
Another fun problem was about dividing the circle into 19 triangles such that at each vertex of the newly formed figure (and also at the vertices of the original triangle) the same number of sides meet. Also if it was possible to divide the original triangle into less than 19 assuming the same conditions.
The first problem was about a variation of Pythagoras theorem x^n+y^n=z^n we had to prove that of n>z then no solution is possible.
The other nice problem was about given 4 random points (non collinear) a, b, c and d and it was asked to prove that if it is always possible to draw circle which can contain the 4th vertex inside the circle. We should recall that if there are 3 non collinear points they always define a unique circle.
Another fun problem was about dividing the circle into 19 triangles such that at each vertex of the newly formed figure (and also at the vertices of the original triangle) the same number of sides meet. Also if it was possible to divide the original triangle into less than 19 assuming the same conditions.
posted by Sumant at 10:57 PM
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