#visualizingmath

Visualizing Math Has Reached 100,000 Followers! Thank You!!! 

When I started this blog shortly after my sophomore year in high school, I had no idea it would eventually become this well-liked. Thanks for enjoying math’s beauty with me and the rest of the math blog community! Also, thank you to the Tumblr @staff for all of your support, and @we-are-star-stuff for being one of my very first supporters! Also, I’d like to take this opportunity to plug the awesome book that inspired me to start blogging: Clifford Pickover’s The Math Book. Check it out!

A little about me: I’m a freshman at Stanford University currently hoping to major in Computer Science. College has been pretty hectic so far, which explains why I haven’t been able to post on here as often as I used to, but I’m still hoping to eventually produce more content again! Also, I hope to once again open up my (very full) ask box—I miss interacting with followers. 

*In response to questions/submissions in my ask box regarding the Klein Bottle*

As you might already know, the Klein bottle is a non-orientable object that has the interesting property of not having an inside and outside (I don't know how to word this better). The Klein bottle is related to the Mobius strip, which is a non-orientable surface that has the property of only having one side. In fact, if you cut a Klein bottle in half, you'd find yourself with two Mobius strips! 

Anywho, I've been getting a lot of messages about whether or not one can make a Klein bottle. The answer is basically "no". One cannot make a true Klein bottle. We can only make things that look like a Klein bottle. The fact of the matter is that Klein bottles can only exist in 4 dimensions where an object is allowed to pass through itself without the presence of a hole. If you look at a 3D Klein bottle (or a 2D drawing of a 3D Klein bottle like the one above), the neck of the bottle has to pass through itself. This is called a self-intersection. Above, I've circled where the Klein bottle self-intersects. It is this self-intersection that renders 3D and 2D unable to be considered true Klein bottles.

3D and 2D representations of Klein bottles do serve important purposes, however. They help us to visualize/understand the Klein bottle, and they look super cool: 

Submitted by Wht-rabbit-obj: "Visualizing Math" written in Gallifreyan.