proof of Aristarchus' Theorem geomterically

Oct 2012
2
0
USA
Hello,

I have been trying to find out if 'Aristarchus' Theorem' can be solved geometrically.

It states that if 0 < α < β < pi/2 then Sin(α)/α > Sin(β)/β

Can you folks think of a possible way of proving this geometrically ?

Many thanks
 
Oct 2012
61
3
India
How about a unit circle? The length on perimeter is equals to angle theta, and the side approximating it in the right triangle will be sin(theta).

Salahuddin
Maths online