Stereographic Projection Tutorial Using Line Parametrization

An all-in-one tutorial on how to parameterize lines and how to stereographically project a sphere to a plane using a given-find-solution style of teaching. What more can you ask for?

I'm saving topics such as the "point at infinity" and why this projection is a homeomorphism for future videos.

This type of projection is important to me because it serves as a "viewing window" into the fourth dimension. In math, we're allowed to stereographically project between n-dimensional spheres and n-dimensional planes. Because of this generalization, the hypersphere of which is naturally embedded in 4D space can be projected down to the entirety of 3D space.

After viewing the stereographic projection of the 3-sphere's Hopf Fibers down to 3-space, it lead me to believe that this projection's greatest purpose lies in its ability to show them.

[adityabaghel]

Wow every little detail explained so wonderfully I'm amazed! Looking forward for new videos. Great job

[curtischee]

Very good presentation. I am doing self study on manifolds. S^2 is an example of a manifold, so your video was very helpful. I hope you do videos on manifolds.

[manuspillai]

You should get more views. Great content!

[aaronTNGDS]

Great presentation. Clear and concise.

[Apubams]

Thank you a lot, I've been looking for these explanation for long time, you made an excellent work. Amazing!

[PSPS]

Nice was able to apply this for a game using a semisphere and projecting a map.

[erikross-rnnow]

Yo! Thank you so much - this was an amazing introduction to this topic for me. I was really struggling with this in my textbook's exercises and you made it sound so simple! YOU A REAL ONEEEE

[jonbovi-]

Subscribed! Thank you so much. This is very helpful and was a clear and great explanation.

[danielbiernat]

That was an amazing explanation, thanks so much!

[Gerardog]

Clear explanation. Great animation. Well done! 🔥

[jason_liam]

Great video . How can we do this for a circle and a line? Can you create a video for that. Thanks. Your channel deserves more subscribers and views.

[ebshadow]

Hi! first of all thank you for this video its great.
I have a question can we use Spherical coordinate system paramets for 'p' and still is it Possible to make Stereographic Projection for that?

[uptodate]

Please this is important for me!!
Let P= [0.7 0.6, 0.5]
Then, by applying Qx = 2*px/1-pz, and Qy= 2*py/1-pz:
Qx= 2.8, Qy= 2.4
On reverse (obtaing px, py)
Px = 4*Qx/qx² + Qy² + 4 = 0.6363 (which is not the real px above), similarly
Py= 4*Qy/Qx² + Qy² + 4 = 0.5454 ?!
Am I substituting wrongly in the equations ?!

[MGoebel-ce]

Try making pauses in between your sentences. Your audience might feel as if you are slapping them. Maybe cut out a little bit of generality instead to keep the video short, guessing that was the goal for the haste:)