Conundrums

 

 

 

The situation is that as soon as the number is expressed as a geometric sequence, its infinite sum is a limit, not the number that we started with. That is, 0.9999999… is not a limit, it is an “exact” value, despite the fact that there is an infinite number of the digit 9.

In fact, neither of the large triangles is actually a triangle. This is because the gradient of the line of the hypotenuse of triangle A (8/3) is not the same as the gradient of the line of the hypotenuse of triangle D.  (5/2)

The diagonal of the rectangle is not actually a straight line. Drawn accurately, it looks like the ‘rectangle’ above.

The missing 1 square centimetre is the unshaded part.