Say we have a circle C1 with radius 2. Inside of that we draw circle C2 going from the centre point of C1 to the perimeter of C1 (making it diameter = 2)
Let A = a quarter of C1 Let B = area of C2 (inner circle)
Is it true that the the areas are the same?
Prove that A = B
A = (pi * r ^ 2 ) / 4 = (pi * 4) / 4 = pi B = pi * r ^ 2 = pi * (2 / 2) ^ 2 = pi
Is this correct?
If this is the case, then with flexible walls, 4 circles of diameter equaling the radius of the outer circle, would fit in the larger circle (Assumption#1)
So this means that the perimeter of A and B should also be the same, since when we squeeze the 4 circles inside the big one the shape will change from a little circle to a quarter circle
Perim A = (arc / 4) + r + r = (2 * r * pi ) / 4 + 2 r = (2 * 2 * pi ) / 4 + 4 = pi + 4 Permin B = 2 * r * pi = 2 * (2/2) * pi = 2 * pi
pi + 4 != 2 * pi This shows the the circumference of A (quarter of big circle) doesn't equal B (smaller circle)
I am practicing and relearning maths after a long break, so not sure if there is something wrong with the numbers, or is assumption#1 wrong?