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Geometry Level 4

In an equilateral triangle with side length 1, consider dropping a perpendicular from a vertex onto the opposite side. Then, repeat this process, spiralling in clockwise, as in the picture. Where ( in Cartesian coordinates, calling the bottom left vertex the origin ) is the point to which this process converges?

suppose the coordinates comes as ( a , b ) (a,b) , submit your answer as a 2 + b 2 a^2+b^2 to 2 decimal places.


The answer is 0.21.

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1 solution

Nilav Rudra
Feb 17, 2016

for information the coordinates are 8 19 \frac{8}{19} , 2 3 19 \frac { 2\sqrt { 3 } }{ 19 }

If anyone can help me with a solution to this question i will be really grateful to him. I know the question and answer but not the solution to this question.

nilav rudra - 5 years, 3 months ago

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