https://youtube.com/shorts/_Anau49e1qk?si=4bXB7F6gEz2_q1xi

Made an animation to show why rockets need stages.

YT: https://youtube.com/shorts/ZoqflzDMW0M?si=GbX9xPveVXFXMJrx

Hi everybody, this post relates to my other 3blue1brown post

But I think this result is significant enough to deserve it's own post.

Let me cut to the chase and say that I have a function which generates primes, and also twin primes. It doesn't even require certification it automatically already knows what is prime and what isn't through the recursive generating structure of the function.

The function counts in mods, but not just any mods, mods of prime numbers. {But those prime numbers don't need to be entered, they are generated by the recursion automatically} This generates the same structure I previously talked about in 3blue1brown reddit and had 14k views and little to no negative feedback.

I have rewritten the paper from the previous post in a much shorter and more clear process now, with less complicated unnecessary language.

I also created a python file to show exactly how it works, in the video you can see me in real time calculating the amount of twin primes in a given number, extremely fast. I could have also listed them all, which would slow the process down ofcourse.

This small python file can tell you exactly how many twin primes are in any given number and it does so without needing to check if they are prime, it already knows based on how they were generated.

It's really just a simple recursive loop counter, mod p, and the golden ratio and silver ratio just fall naturally out of it.

Here is the updated paper

and here is the github for the python file to test what I did in the video yourself

Edit{I am also hosting the paper on my own site if the zenodo link isn't working.}

https://www.youtube.com/watch?v=yakGJwuYCdM

So I have always been into simulating fluid dynamics and made this visualisation to show how heart disease progresses.

Computational Fluid Dynamics has so many applications!

YT: https://youtube.com/shorts/YeEj1JfpKs8?si=OG-xE7ysSOfoKCoH

Made an animation on Second Law of Thermodynamics, it doesn’t have true molecular dynamics simulations, just simplified kinematics to represent them.

Check it out on YT: https://youtube.com/shorts/uYoFgwXZ5BY?si=NId3BBLzHPk_4Kqh

I was solving Gilbert Strang's Introduction to Linear Algebra, and Problem 32 of Section 1.2 says to select a random 3-component unit vector, let's call it v, then generate more such vectors, and solve for the average size of the dot product of all these newly generated vectors with v.

When I simulated this with Python code, I got approximately 0.5. However, at the end of the problem statement, it says the calculus average is 2\pi. I guess the book's hint is based on the continuous expectation $\int P(\theta)\vert{}\cos\theta\vert{}d\theta$ written as a standard 1D integral. But because these are 3D vectors, we are essentially sampling points uniformly from a unit sphere. The probability density must therefore be given by the surface area element of that sphere, which introduces a sine factor to the distribution. When I calculate the expected value using this spherical surface weight, it yields exactly 0.5, matching the simulation.

I just want to discuss this.

Made an animation on the First Law of Thermodynamics:

https://youtube.com/shorts/mx53f0d2bVE?si=4sCkkdm4bS4lYxbM

The ISS isn't in some gravity-free pocket of space — at 400 km up, gravity is still about 90% of what it is at Earth's surface (g ≈ 8.7 m/s²). Astronauts float because the station is permanently falling: moving forward fast enough that the ground curves away beneath it before it ever hits. Newton captured this geometrically in 1687 with his cannonball thought experiment — fast enough, and "falling" and "orbiting" become the same motion.

The full carousel goes one step further: why free fall feels weightless at all. Gravity pulls on every atom equally, so there's no floor pushing back and nothing to generate the sensation of weight — even though gravity is still fully there.

Dm me with your videos you made with manim or any other

Hello,

If you've ever worked with gradient descent, you know the basic goal: step downhill until the slope is zero. But a flat slope (a zero gradient) is a trap, it could be a local minimum, a maximum, or a saddle point.

I made a visual breakdown of the mathematical machinery we use to test for true minima. The video is an intuitive, 6-minute refresher on how gradients, Hessians, and contour maps actually work behind the scenes of your optimization algorithms.

Made an animation on Zeroth Law of Thermodynamics. Do check out the full version on YT: https://youtube.com/shorts/KNOyTMb3Nqs?si=DCSBoC0xhdt77ujC

The visual intuition behind banked roads (and why mass doesn't matter)

When learning about circular motion, the physics of banked curves is often taught as an exercise in algebraic substitution, but there is a really beautiful geometric intuition happening here.

If you imagine driving on a completely icy, frictionless banked road, the only thing keeping the car in a circle is the tilt of the road itself.

Visually, the Normal Force (N) is doing all the heavy lifting, but it splits into a perfect right triangle of components:

• The vertical component, N cos α, perfectly opposes gravity (mg).
• The horizontal component, N sin α, points directly at the center of curvature, effectively acting as an invisible tether—the centripetal force.

When you set up the equations visually, you get: N sin α = mv² / R N cos α = mg

If you divide these two, the normal force (N) and the mass (m) completely drop out of the geometry, leaving us with: tan α = v² / (gR)

I created an animation to visually break down exactly how these force vectors shift and scale as the banking angle changes, showing exactly why a massive truck and a tiny bicycle are bound by the exact same geometric constraints and speed limits on an icy curve.

Would love to hear how others visualize this concept when teaching or learning it!

3b 1b has all these videos on differential equations, calculus, linear algebra, etc. But how come he doesn't have one for discrete math? He's talked about computer science stuff before; I don't see why he would skip over it.