Keep constructing triangles in the incircle of the previous triangle. What happens?
Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Well done Geoffrey, University College School, London for this
This problem is actually remarkably straightforward. A little
bit of algebra is all that is needed.
Let x and y each denote 1 of the 2 numbers to be multiplied
The layout of the grids in the question then corresponds to:
The 4 ways of calculating the left hand digit are expressed
algebraically as follows:
All 4 ways are algebraically equivalent, so this is why they
give the same answer.
To explain why the Vedic Sutra works, we run through the whole
The right hand digit is ( 10 - x ) * ( 10 - y ).
The left hand digit is ( x + y - 10 ). We should remember that this
is the tens digit and multiply by 10 before summing both sides.
10 * ( x + y - 10 ) + ( 10 - x ) * ( 10 - y )
= 10x + 10y - 100 + 100 - 10x - 10y + xy
Using the Vedic Sutra, we get the result xy, which is indeed the
product of x and y.