An animation of six fundamental types of integrals used in mathematics, physics, and engineering
For code click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Visual_Guide_to_Calculus_Integrals.ipynb
I made a visualization of cofactor expansion for a 3×3 determinant.
The idea is to start with the usual interpretation of det(A) as signed volume, then show each cofactor term as:
• one coordinate projection of the expansion column
• one projected 2×2 minor in the orthogonal coordinate plane
So instead of treating
det(A) = a₁₁M₁₁ − a₂₁M₂₁ + a₃₁M₃₁
as only a symbolic rule, the goal is to make the three terms look like signed volume pieces.
The image shows the three terms for one example matrix, including the “same sign / negated sign” behavior of the cofactor signs.
Full explanation, including determinant sign:
https://www.graphmath.com/la/determinant/determinant-sign.html
I would be interested in feedback on whether the geometric interpretation is clear
I was trying to dip my toes in machine learning and my understanding was to build a solid grasp on algebra, calculus, probability and stats beforehand. I'm good with the maths portion now but it's confusing where to go next to actually make an actual model that utlises all these things. I'm trying not to build everything through AI/chatbots just to get a better understanding of the material that I want to work on
This is a genuine ask for feedback and your guys honest initial thoughts on this.
The idea: episodic, narrative-driven games where you play as a historical mathematician (Euler, Ramanujan & Hardy, Emmy Noether, Al-Khwarizmi) and work through the actual problem they were trying to solve, in the historical context they were in. This would NOT be a quiz. Not "here's the theorem, now answer questions about it." More like: here's the problem as they faced it, with the same partial information, the same wrong turns, and the same dead ends. You follow the reasoning as it actually unfolded, focusing on Interactive discovery.
FAIR WARNING: A question that I think we often get is “how will this teach mathematics?” and the answer is: it won’t. This would NOT be an education game that teaches you maths, or even the entirety of maths history. It humanises mathematics, and tells the story of certain figures within maths history, hopefully showing that mathematics is a very important part of our history not just for the field itself, but for us as humans. Eventually, we’d want this to reach people who may not be entirely interested in maths, but still interested in the history and the narrative, and show that maths is not just about adding numbers together.
The audience we're imagining is basically: people who watch 3Blue1Brown, Veritasium and other science / mathematics content, who come away wanting more depth, more context, more of a sense of what it actually felt like to be inside these ideas.
But here's what we genuinely don't know:
- Is a game even the right format for this? Or does the interactivity get in the way of what makes these stories compelling?
- Would you actually want to do the maths, or do you prefer being shown it?
- Does putting you in the role of the mathematician sound exciting, or does it sound exhausting/boring?
- Is this something people want alongside videos like 3B1B (a different kind of experience) or does it feel like it's trying to unnecessarily replace something?
- What would make you instantly close it and never look back?
- Who would you want to know the story of? (we wanted to start with mathematicians, but eventually branch out into scientists, or whoever else might be interesting to the players)
Some more important points: this would be team-built and funded, so not a scratch game, and part of this team would be experienced mathematicians and maths historians so we’re not just reading the Wikipedia page to write the story. We also want this to be as authentic as possible. We think history is fascinating and dramatic organically, so there is no need to add lies and warp events just to make them more “entertaining” (although, as with a lot of history — especially the ancient kind — there will be moments where different sources say different things and human bias makes things complicated, so our goal is for this project to be heavily community based, with many decisions falling onto you). Okay, that is all.
We're pre-build so we don’t have a demo or anything, we’re just trying to figure out if we're solving a real problem or inventing one.
Did this for YT: https://youtube.com/shorts/jNn49bjIWzk?si=dhJGSFPtw4lntdFP
Really happy how the colour gradient came out!
Recently got my script-to-manim animation platform (tensorframes.co) to handle long form videos. Feedback welcomed.
Check out more animations @tensor_frames
So I've been hanging out with a girl for couple of days and her birthday is coming up next week and I have been thinking of gifting her a set of lingerie(dark red with netted design) but I think it might too forward but I have build up the courage now so I need the last confirmation from yall girls.
Here's a stat I found: after watching videos like Veritasium or 3Blue1Brown, around 74.31% of viewers say they go on to explore the topic further after watching. (https://www.frontiersin.org/journals/communication/articles/10.3389/fcomm.2020.600595/full)
I think this is good because it means that people probably aren't just passively consuming and moving on. They're clicking links, and reading articles and I think that’s a good sign for science communicators, and in general.
But one question that I do constantly have is ‘does any of it actually stick?’
Because I notice in myself (and I'm curious if others do too) that after I watch a really well-made video I do feel like I’ve just learned so much and after I read up on it a little bit more I feel like I actually get the topic and I can even explain it to my girlfriend somewhat. But then a week later I don’t actually remember much, especially the actual reasoning and ‘why’ behind something. I feel like I vaguely remember what was going on, but I definitely wouldn’t be able to explain it.
I don't think that's a failure of the videos. I think it might just be the nature of watching vs. doing. Watching someone navigate an idea is genuinely different from navigating it yourself.
So I'm curious:
- Do you actually feel this? Or does the video format work well enough for actual learning?
- Is going off and exploring further the same as actually learning, or is it just more consuming?
- Should the passiveness of a video even be seen as a problem, or is that kind of the point? You want to be taken on a journey, not put to work.
I’ve been getting into science communication and mathematics education lately as a potential next step, so I would be very interested to know since these videos seem like the most popular format right now.
The Higgs Mechanism, electroweak symmetry breaking, and key particle physics concepts inspired by Feynman Diagrams.
Concepts visualized are:
The Higgs Field
Spontaneous Symmetry Breaking
Gluon Fusion
Higgs Decay to Photons (H → ̳̳)
The Golden Channel (H → ZZ → 4ℓ)
Electroweak Symmetry Breaking
For more animations click www.instagram.com/craftsandengineering
For code and more click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Quantum_Physics_Higgs_Mechanism_Feynman_Diagrams.ipynb
Music attribution: Quantum - PHNKR PHONK & Donovan on TikTok music library
A physics simulation of an inverted pendulum on a cart that evaluates three distinct control architectures—PID, LQR and MPC — on their ability to maintain equilibrium and recover from significant external disturbances.
For more videos click instagram.com/craftsandengineering, or tiktok.com/@zoomzoombee
Join me on Patreon and claim your free trial lesson: https://www.patreon.com/cw/Hyperbolic_Math_Chamber
Hi guys,
Just wanted to say thank you for all the positive feedback from my first post about Linear Algebra Visualizer.
Especially from u/LongjumpingEar7568 and u/Ron-Erez who suggested adding the eigenvectors and values. This is now complete and I’m excited to share it with you guys in this community.
This update includes:
- Explore eigenvectors and eigenvalues visually
- Polygon presets
- Enter any 2x2 matrix
Thanks for your supports and let me know of any feedback in the comments please :)
Available on the platforms below:
Mac: https://apps.apple.com/gb/app/linear-algebra-visualizer/id6763524968
iOS/iPad: https://apps.apple.com/us/app/linear-algebra-visualizer/id6763524968
Web: https://sockerjam.github.io/LinearAlgebraVisualizerWeb/ (Eigenvectors and values coming soon!)
An animation of the Feynman Path Integral, visualizing the Principle of Stationary Action.
For more videos click www.instagram.com/craftsandengineering
Inspired by this post on X https://x.com/scievision369/status/2055314591270436884?s=20
A high-fidelity, visually engaging animation illustrating the mathematical beauty and symmetry of inverse functions across the identity line
For more videos click www.instagram.com/craftsandengineering
For code click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Symmetry_of_Powers_and_Roots.ipynb
I'm wondering fi there is a way to purchase the audio only of a youtube playlist so I can listen at work. I know much is lost without the visuals but I don't have time to sit and watch youtube videos and this is really the most accessible way I would likely access the content. Thanks
Hey everyone,
I just published a quick, 5-minute animated guide breaking down the Z-Transform. Instead of just throwing a wall of math at you, I tried to make the concepts actually click.
In the video, I cover:
How the Z-Transform compares to the Laplace transform
Deriving the simplest signals (Unit Impulse & Unit Step)
Crucial properties: Linearity, Time-Shifting, and Value Theorems
A mechanical 3-step engine to solve any difference equation using Partial Fraction Expansion.
Let me know what you think, or if there are any other DSP topics you'd like to see visualized!