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How to Discover Euler's Formula by Yourself (In About 2000 Years...) #32

Open saroad2 opened 2 years ago

saroad2 commented 2 years ago

About the author

My name is Sagi Shadur. I'm 27 years old from Israel. I have a bachelor degree in Mathematics and this year I'm finishing a second Bachelor degree in Physics. I'm a software engineer and currently work as a Machine Learn Team Lead at Proxima Investments ltd.

I love science and mathematics content and I watch it regularly on Youtube. I watch 3blue1brown, Minute Physics, Seeker, Numberphile, Mathologer, Be Smart, Veritasium and many others.

Besides all of that I'm a published poet. I wrote three books published in Israel named "Mountains and Hills" (2018), "The Emissary" (2020) and "Mad New World" (2022).

I wanted to make my own math videos for quite some time now, and this is a great opportunity for me to try to do so.

Quick Summary

Euler's Formula is one of the most beautiful formulas in math. People have made hundreds of videos about it, however most of them explains what Euler's Formula is and how to prove it without taking the time to talk about the history of how it was discovered.

In my project I want to take the viewers on a journey from the ancient Greeks to Euler and show how one discovery led to another, finishing in Euler's amazing formula. In my project I want to talk about:

  1. Thales's theorem and the discovery of the trigonometric functions
  2. The expansion of the trigonometric functions to the entire number line using analytic geometry, the Pythagorean theorem and the unit circle.
  3. How replacing degrees with radians is actually good for calculations.
  4. Showing the intimate relationship between trigonometric functions and the number i and give some clues that will later reveal Euler's Formula.
  5. Finally, proving Euler's Formula using everything we talked so far and Taylor series.

Target medium

I would like to try to put everything into one video, but realistically I think the best approach is to create a playlist of multiple videos, each about a topic presented above, all leading to proving Euler's Formula.

More details

I will do the narration, but I want the video to be entirely animated. I want to show everything visually so it will be as easy to understand as possible.

Contact details

One can contact me:

Hebbmat330 commented 2 years ago

How long would each video be?

saroad2 commented 2 years ago

I hope we can make the videos about 10 minutes each. I assume that 1 and 5 will be the longest, 3 will probably be the shortest

Jorgeromeu commented 2 years ago

I don't think I'm qualified to make the videos, as I still can't claim to fully understand Euler's formula, but really look forward to the final video, this sounds really cool

saroad2 commented 2 years ago

Hey @Jorgeromeu , thanks for the feedback!

In regards to the mathematical knowledge needed for making the videos, I think I got this covered :) I just need someone with excellent skills in Blender or any other animation software to show the relevant demonstrations. I want this videos to be very visually oriented.

Hebbmat330 commented 2 years ago

Hey I can't promise I am incredible at blender but I would be more than happy to try to help out in anyway I can. I've done a lot of 2d animation and video editing but I've been wanting to practice 3d more so if you are willing I think we could make something pretty cool.

saroad2 commented 2 years ago

Hey @Hebbmat330.

Cool! Let's talk. Send me an email with some details about you and your experience and we can continue from there :)

I don't think we need 3d animations here. Most of the subjects are geometric in nature and relevant only for the 2d plane, so I think we are good!

Jorgeromeu commented 2 years ago

Hey @saroad2,

I have some experience with blender scripting, I feel like that could be a really nice way of making visuals of geometry, as it can be controlled programmatically (like manim) but is maybe more flexible, as even though we can mostly limit ourselves to 2D, since its blender, at any moment we can move to a 3D view, which could be cool for complex number things. If its useful I would be up for taking on some of the animation load :)

saroad2 commented 2 years ago

Hey @Jorgeromeu .

I think this is one of those projects where the more people are involved the marrier :)

Please send me an email with some details about you and your experience and maybe we'll try to schedule a Zoom meeting of the three of us.

If someone else wants to join, please let me know.

saroad2 commented 2 years ago

Project update:

@Hebbmat330 and I started working on the scripts for the 5 videos. We are currently working on video number 4. Once we finish that, we'll start working on the actual videos. We estimate that the videos will be about an hour long in total.

There's still a place in our team for anyone who wish to join and can help us. We need:

  1. Peer review for the scripts
  2. Animators and video editors for the videos

If someone is interested, please let us know!