N-gated Hacker NewsOct 1
Oh, the profound wisdom of expanding your "practice surface area," because clearly, success is just a matter of stretching that metaphorical #yoga mat of #mediocrity a few inches wider. 🙄🔍 Spoiler alert: it's still just a fancy way of saying "practice more," but with extra #buzzwords to make you sound like a self-help guru. 🧘‍♂️💡
https://www.indiehackers.com/post/lifestyle/increasing-your-practice-surface-area-agxYGi9bL0gd1WYYQZAu #expandingpractice #surfacearea #selfhelp #HackerNews #ngated
Increasing your practice surface area

The difference between good and great isn’t talent or formal training, but the invisible practice that happens when you're just living life.

Indie Hackers
HaraldAug 1, 2024

Today I wondered what the surface area of a ball is, well not if it lives in normal Euclidean Space where it is 4\pi r^2, but if it lives in a space which itself is a 3-sphere and the radius of the ball is of course measured in that curved space.

More detail: https://math.stackexchange.com/q/4953206/121890

#math #mathematics #manifold #surfacearea

Within a space which is a 3-sphere, what the is surface area of a 2-sphere?

If an ant lives on a ball (2-sphere) with radius $r$, draws a circle and measures the radius of the circle as $R$ as it walks along the ball's curved area, it will find that the length of the circl...

Mathematics Stack Exchange
Pustam | पुस्तम | পুস্তম🇳🇵Jul 28, 2024

Math makes ‘obvious’ things false. Imagine an object with finite volume but infinite surface area. Gabriel’s Horn is an interesting and beautiful object with infinite space but finite volume. It is explained as “you can’t finish Gabriel’s Horn when you want to paint it, but if you put this much paint in it, you can fill it so that it will be painted.” It is formed by rotating the \(y=\frac1x\) graph around the x-axis. There is a nice demonstrative project on Wolfram Alpha about Gabriel’s Horn. [Link: https://demonstrations.wolfram.com/GabrielsHorn/] Also, if you want to read more about “Paradoxes of the Infinite”, you can check Paolo Mancosu’s book, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. [Link: https://www.amazon.com/Philosophy-Mathematics-Mathematical-Practice-Seventeenth/dp/0195132440]

#GabrielHorn #SurfaceArea #Volume #CounterIntuitive #Maths #Mathematics

Gabriel's Horn - Wolfram Demonstrations Project

Gabriels Horn is obtained by rotating the curve around the axis for Remarkably the resulting surface of revolution has a finite volume and an infinite surface area It is interesting to note that as the horn extends to the volume of the horn approaches