In this last episode on non-Euclidean geometry, I present the opposite of the spherical geometry, i.e. hyperbolic geometry. This hopefully will give you additional intuition of straight lines in curved spaces…

# What’s a straight line? Curved-space geometry | Science4All 10

StandardStraight lines in curved spaces are highly counter-intuitive, but they are the key to general relativity! Now, many mathematicians and physicists would say that they are distance-minimizing trajectories, which is (almost) true. But, like Gabe on PBS Space Time, I actually don’t like this definition. I think it is neither natural nor insightful… Here’s why:

What do you think? Do you get a feel for straight lines in curved spaces now? Are there things that are troubling you? Tell me!

# What’s wrong with that map? Spherical Geometry | Science4All 9

StandardAfter two episodes about flat surfaces, finally, Episode 9 introduces curved geometry. But we start easy, with the most familiar of all curved spaces: the sphere. Interestingly, the geometry of the sphere has played a crucial in the History of world conquest by European nations…

So, which is your favorite map? Are you deeply disturbed by the upside-down Mercator map? What about he butterfly-shaped map?

# Why do soccer balls have the shape they have? Platonic solids | Science4All 8

StandardEpisode 8 here is quite a detour on the way to general relativity. It’s about a very cool piece of geometry that’s embedded in the well-known shapes of soccer balls.

So, how many panels will the 2018 world cup be made off? What’s your bet?

# Can you glue opposite edges of a square? Nash’s embedding – Science4All #7

StandardI’ve long regarded my 7th video as my best video. It has plenty of pretty cool stuffs inside it: concrete simple problem, Historical anecdote, well-known scientists, awesome mathematics, recent developments, stunning images… Most importantly, the video introduces the very basics of curved-space geometry, through Nash’s fantastic embedding theorems, with a particular focus on the duality by intrinsic and extrinsic approaches to geometry.

There’s a somehow unfortunate story behind this video: I uploaded it the day before John Nash, a central mathematical figure of the video, sadly passed away. This has led me to make a follow-up video dedicated to Nash, where I also apologized for the somewhat not-very-respectful way I presented it here. In the end, I truly admire the man. Both for his life struggle with schizophrenia, and his epic mathematical journeys.

To this day, this is the video of the series that has had the most views (1.4k). I must say, though, 1.4k views is not a lot. My best earlier videos have 10k, 20k and even 40k views… So, the question I want to ask you is: How do I get more views? How can I improve the videos? Are there things in the videos you did not like? Are there things you did not understand?

# Is special relativity relative? Space contraction and time dilation – Science4All #6

StandardSo this was the first actual episode on relativity. But only special relativity.

This video is pretty classic and there are a dozen of similar videos on youtube. I did it because I just had to do it. You know… on the way to general relativity. Still, if you have remarks/questions/criticisms… etc, I’d love to hear it!

# Science4All on Youtube

StandardFor the last six months, I’ve been doing a new series of Youtube videos on my Science4All Youtube channel. Initially, my goal was to, in each video, start from a basic question, and get to a fundamental concept of mathematics or science. Here’s the first video of the series (it was the first, so please be tolerant^^):

Quickly enough though, after the third of fourth video, my personal taste for the big ideas of mathematics and science, rather than fun but non-big-picture facts, has led me to set another goal. Instead, since then, I’ve been establishing the basic tools to have an insight into one of the greatest achievements of the human minds, the theory of general relativity. Clearly, this has got me much more excited about making these videos, and I think you can feel this in this fifth video of the series:

I’ve gone a long way since. By now, as I’m writing this post, the 15th video — the big finale — has just come out. Here it is:

Of course, this last video is very hard to understand if you haven’t watched previous ones. So, every day in the next week, I will repost the videos, with maybe some additional comments.

What I would love is some feedbacks on the videos. I must say that I’m frankly disappointed by the number of views the videos have had so far — only two have reached 1k views — and the lack of comments left on Youtube. In particular, I’ve been very impressed and inspired by the PBS Space Time series that, amusingly, set itself the same challenge as I did, namely, explaining general relativity through a collection of build-up videos. Gabe (and now Matt) picks up interesting questions and remarks of the Youtube comment section and reply to them in the follow-up videos (both are actual astrophysicists, so they can actually give in-depth replies to tricky questions… which I cannot!). As well, I’ve recently discovered the channel Looking Glass Universe, where “she” (I don’t know her name…) actually gives “homework” in the videos, and gets a lot of replies.

Since I don’t seem to have enough viewers so far to do so, maybe here would be a good place to start. Tell me what you think!