Problem / game
First name
Nikhita
School
St Stephens
Country
Age
15
To prove that the area of each n-coloured circle is equal.
The proportion of each in each shape: n= no. of shapes within circle, x=radius
(Ï€x^2-1/nx^2) /2
As the radius of the smallest semicircle is twice the size of the second smallest semicircle, thrice the size of the third smallest circle etc... the original formula must be multiplied by the size of the other semicircles:
smallest semicircle= πx^2, second smallest= 2πx^2, third smallest= 3πx^3 etc.
Therefore all sections have equal area for a circle with n sections as:
smallest semicircle= πx^2/2, second smallest= 2( πx^2/2) etc...