What are some mind-blowing facts about mathematics?

What are some mind-blowing facts about mathematics? by Sandipan Bala

Answer by Sandipan Bala:

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

Edit: Updated the images corresponding to the GIF file, since GIF file is not accessible on Quora for mobile devices.

What are some mind-blowing facts about mathematics?

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