And it doesn’t have an edge. Or, as the... - Deepstash

Explore the World's Best Ideas

Join today and uncover 100+ curated journeys from 50+ topics. Unlock access to our mobile app with extensive features.

And it doesn’t have an edge. Or, as the mathematicians would say, it doesn’t have a boundaryA Klein bottle is also a hollow tube whose ends have been joined. However, before the ends are joined one end passes through the wall of the tube, like a ghost through a wall, and travels down the tube to meet the other end.

It is important to realize that the wall of the tube is not breached it remains intact and continuous. This is possible because a Klein bottle is a shape, an abstraction, and not a material object.

1

0 reads

MORE IDEAS ON THIS

Klein bottle

Klein bottle

It's a surface whose top and bottom are the same (non-orientable object). So, the Mobius strip is a one-sided strip (non-orientable). The Klein bottle extends this to the next dimension, which takes the object into a fourth spatial dimension. People only observe three spatial dimensions. Projecti...

1

1 read

Klein bottle” sounds like it should be an object of some sort. But it’s not. It’s a shape. Moreover, in three dimensional space.

The closest shape to a Klein bottle would be a torus. A torus is the shape of a doughnut or O-ring. It is a hollow tube whose ends have been joined. As a result ...

1

1 read

More like this

Be intentional about your breakups

You will go through a lot of different versions of yourself. It can mean that a friend is only there for a certain chapter, and that's OK.

When a friendship ends, it's good to be intentional. State that you want to end the friendship and talk about what that means in pract...

ANGELINA JOLIE

What’s one piece of advice I have for someone going through a hard time?

Go right through it. Like, right through it.

Feel it. Be in it. Don’t avoid it. Go completely in it, feel everythi...

ANGELINA JOLIE

Outline a beginning & an End

Outline a beginning & an End

Outlining is a visual process that shows the beginning and the end. It’s taking something abstract and making it visible.

Try starting at the end. Write what your idea will accomplish or what you want it to accomplish. Then work backward. This gives your id...

Read & Learn

20x Faster

without
deepstash

with
deepstash

with

deepstash

Access to 200,000+ ideas

Access to the mobile app

Unlimited idea saving & library

Unlimited history

Unlimited listening to ideas

Downloading & offline access

Personalized recommendations

Supercharge your mind with one idea per day

Enter your email and spend 1 minute every day to learn something new.

Email

I agree to receive email updates