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Summer of Math Exposition

Metric Spaces

Audience: undergraduate

Tags: real-analysismetric-spaces

This website is a visual and interactive exploration of metric spaces, intended for a broad audience. Anyone somewhat comfortable with high school algebra should be able to follow along and enjoy a new and exciting field of mathematics. Those with prior experience will hopefully enjoy the visualization and strengthen their intuition. Enjoy! :)



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7.9 Overall score*
3 Rank
16 Votes
12 Comments

Comments

8.9

I love the interactivity. Super clean and neat! Builds up concepts from the ground up!

6

Clear explanation with nice diagrams. I assume you ran out of time trying to complete this.

8

Excellent at what it is; serves as a great intro with clear graphics. What I would have liked would be some more “problems” for a student to answer (eg. move the point into the space, select which would be on a boundary, etc.) but otherwise amazing job.

8.3

The images and the ability to zoom in are perfect for presenting metric spaces. I will save this for the analysis courses.

8

High quality, well done, keep it up!

8

I really love your interactive! A very well-made visual presentation of metric space. The aesthetic works really well with clarity of your explanation. A student like me can learn at my own pace with your interactive. I also love the fact that you stop occasionally to makes the reader ponder and think about it first before continuing. Bravo!

7

A very beautiful interactive slideshow.

8.5

I didn’t work all the way through this but I was really impressed with what I did get through. I have no prior experience with metric spaces and I understood everything very well. There is a nice progression following a clear direction, and it’s beautifully presented. A couple of technical things that I took issue with and would make things even better if improved:

  • The contrast on labels for distances is shockingly low. Text on the coordinate grid really needs to be a much darker grey and shouldn’t fade out quite as much.
  • I found myself highlighting the text when trying to drag a point a couple of times - ideally the text should be non-selectable, or, even better (in my opinion), just get rid of the fade-out transition and have the coordinate grid be in its own clearly defined box, to avoid any possible confusion.
  • On some mobile devices the text could overflow and it doesn’t scroll; if the text covers the draggable bits this also causes problems.
9

I really enjoyed your website so that I’ve bookmarked this for future reading. I think you did an excellent job with setting a focus for students who’d like to learn metric spaces, and broke these pieces down into digestible parts. I think of this as next-gen “Paul’s Online Math Notes.” I haven’t scored a perfect 9 until I came upon yours. Your Ranking score was based on an average of these individual categories:

Motivation: 9 Clarity: 9 Novelty: 9 Memorability: 9

7.7

Amazing diagrams - I particularly loved the “compact sets are closed” animations - you have inspired me to animate my own topological proofs!

Since the content is so granular (slide-by-slide), I felt a bit gridlocked to reading at a slower-than-ideal pace in some places.

7.5

Webpaga should work better on mobile or at least have a disclaimer.

As for the content itself it is good and detailed, the depth is consistent all throught and it helps build intuition with the examples

7.4

Very innovative exposition