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area of sphere




Well ever wondered how the Surface Area of a Sphere was derived?
Well here is a great visualisation to alter your perception.
Step 1: Cut the sphere in the following way.
Step 2: Spread the cut out part across the paper
Step 3: Collate the pieces together in the following way
Step 4: Spread the areas out separately to form a sine curve
Step 5: The area of the sine curve is the surface area of the sphere
Here’s a GIF file for better understanding.
There’s of course the generic method of calculation where the surface area is calculated by cutting the sphere into infinitesimally thin disks of varying radius stacked over one another and integrating them, but this above method is a different way to look at the same problem.
Image Source: Google Images

220 Loves 284.
Yes, this pair of numbers was considered as a symbol of love in medieval period, lovers used to send flowers, fruits to each other with these numbers written. Also some Arab writings say that couples used to eat apples with these numbers written and believed that it increases their affection and seduces them.
These are called amicable numbers, a pair of numbers, each of which is the sum of the factors of the other. The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.[1]
The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992)[2]
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