Gabriel’s Horn

Math makes ‘obvious’ things false. Imagine an object with finite volume but infinite surface area. Gabriel’s Horn is an interesting and beautiful object with infinite space but finite volume. It is explained as “you can’t finish Gabriel’s Horn when you want to paint it, but if you put this much paint in it, you can fill it so that it will be painted.” It is formed by rotating the y=\frac{1}{x} graph around the x-axis. There is a nice demonstrative project on Wolfram Alpha about Gabriel’s Horn. You can check it out here. Also, if you want to read more about “Paradoxes of the Infinite”, you can check Paolo Mancosu’s book, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.

Similar Stuff

1/499999

1/499999

Here is an interesting division 1/499999! If you divide 1 by 499999, you get all the powers of two up to six digits long.
A Real Introduction to Calculus

A Real Introduction to Calculus

This guy wanted to teach his niece calculus and get the book "Introductory Calculus for Infants. The baby's reaction is a real introduction to calculus.
37037037

37037037 

37037037 is a pretty interesting number. When you multiply it with the multiples of 3, you get a beautiful pattern!
13177388

13177388

13177388 is a super interesting number. You can write with the sum of the powers of sevens, and 13177388 = 7¹+7³+7¹+7⁷+7⁷+7³+7⁸+7⁸.

Fibonacci’s Soup

The Fibonacci series is an incredibly harmonious sequence of numbers. Fibonacci's soup is a funny math meme inspired by the Fibonacci series.
Hyperbolic Slot | Cool Math Stuff | Abakcus

Hyperbolic Slot

Common sense tells us that if we have a curved hyperbolic slot and a straight rod, the straight rod can't possibly fit through the curved slot.