Thomae’s Function @MathVisualProofs

Uploaded January 2025 | Updated September 2026, 2 weeks ago

This is a visualization of an approximation of the Thomae's function, which is a function that is continuous at irrationals, discontinuous at rationals, and differentiable nowhere.

To buy me a coffee, head over to buymeacoffee.com/VisualProofs
Thanks!

#manim #math #mathshorts #mathvideo
#construction #calculus #mtbos #manim #animation #theorem #iteachmath #spiral #thomae #continuous #continuity #differentiation #differentiablenowhere #function #irrational_number #irrational #rational #rationalnumbers

To learn more about animating with manim, check out:
https://manim.community

Ulam Spiral (primes in a 450 x 450 grid)!

$Lévy C: Copy; Rotate 90; shift new start to old end Lévy C: Copy; Rotate 90; shift new start to old end In this video, we show how to generate a fractal curve known as the Lévy C curve or Lévy Dragon by repeatedly copying, rotating and shifting, starting with a line segment. What happens if you do something similar with different rotations or different shifts? If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! Check out these videos for related constructions: https://youtu.be/rLxx6b-oJGo https://youtu.be/NBI_5GdvqUo This animation was inspired by an article written by Larry Riddle that appeared in the the November 2016 issue of Math Horizons: https://doi.org/10.4169/mathhorizons.24.2.18 See more here (https://larryriddle.agnesscott.org/symmetricfractals.pdf) and on his website: https://larryriddle.agnesscott.org/ifs/levy/levy.htm #levy #levydragon #math #manim #animation #fractals To learn more about animating with manim, check out: https://manim.community$

Continuous everywhere but differentiable nowhere : Weierstrass Function Visualization!

Infinite Sum of Powers of 1/3 in Equilateral Triangle

Lunes off a Right Triangle (visual proof)

Function Proof via Diagram Chasing (g composed f injective and f surjective implies g injective).