4 ms·

2-D Mathematical Curves

98 points by the-mitr 6mo ago

gpugreg 6mo ago
Related: Wolfram Alpha can generate Pokemon curves: https://www.wolframalpha.com/input?i=pikachu-like+curve https://www.wolframalpha.com/input?i=pikachu-like+curve
- sunrunner 6mo ago
  I'm getting Mimikyu vibes from it.
- soupspaces 6mo ago
  Why disjointed if sum of sines?
  - smithmayowa 6mo ago
    You're killing me if you don't know the sums of sines could be discontinuous, although this property is usually only apparent when you take the sums of a sine series(e.g Fourier series) to infinity. This particular function is composed of a heaveside step function though which is the reason for its disjointedness.
ktpsns 6mo ago
Beautiful and informative website from the old age: Tables, tiling background pictures, no fancy fonts or colors, even the formulas (equations) are typesetted as low-res bitmaps instead of contemporary MathML/JS/etc. For me, it feels like leafing throught an old vintage book (I have plenty of old math books left from my studies). I find it quite funny that clicking "the author" brings us to Linkedin, feels like going back to reality.
seanhunter 6mo ago
This has got one of my favourite curves in maths, the “Witch of Agnesi” https://www.2dcurves.com/cubic/cubicr.html#witch%20of%20agnesi https://www.2dcurves.com/cubic/cubicr.html#witch%20of%20agne... There are 2 plausible stories about the origin of the name for this curve which was used as an example in a calculus textbook by Maria Agnesi on how to do an integral with partial fractions. The website gives one version of the story, that the curve is named after the latin for a coil of rope which Agnesi then turned into Italian as la versaria. The other possibility is that since the curve was in a problem, she meant l’aversaria (our adversary/opponent, but crucially the feminine version of this noun). In any case, when it was translated into English, the person translating said something along the lines of “Well aversario is the devil, so aversaria must mean ‘witch’” and so the curve became known as the “Witch of Agnesi”. This curve (the folium/leaf of Descartes) is also very cool. https://www.2dcurves.com/cubic/cubicf.html#folium%20of%20Descartes https://www.2dcurves.com/cubic/cubicf.html#folium%20of%20Des... Decartes and Fermat had a massive falling out via letters over trying to get a method of deriving the tangents of this curve, with Decartes insulting Fermat because Fermat’s method was insufficiently rigorous even though Decartes was unable to take the tangent using his method and a modern calculus student would recognize Fermat’s method as very similar to the modern definition of the derivative as the limit of the difference quotient. Decartes was very uncomfortable with the fact that it seemed to be dividing by zero.
lorenzohess 6mo ago
I'm really curious what type of people find a practical use case for this? Graphic designers?
- pengaru 6mo ago
  seems like an obvious application would be game development? procedural curve functions are used quite a lot, look up "tweening" for instance.
- soupspaces 6mo ago
  For anyone answering questions like these
ariedro 6mo ago
A glimpse of old times, when the quality of the content mattered more than the presentation.
tobinfricke 6mo ago
Reminds me of the Online Encyclopedia of Integer Sequences https://oeis.org/ https://oeis.org/ But I was somewhat surprised when my first click in this encyclopedia of 2d curves landed me on a 3d sponge https://www.2dcurves.com/3d/3dm.html https://www.2dcurves.com/3d/3dm.html
lioeters 6mo ago
Great collection of curves and articles about them. So many I'd never heard of, I'm enjoying all the pages. The formulae are only in tiny images though, I wish they were in text or MathML. But there's enough information that I can try producing some of my favorite curves and spirals.
leopoldj 6mo ago
There's something wrong with the cartesian equation for scarabaeus [1]. I think it should be: (x^2+y^2) * (x^2+y^2+bx)^2 - a^2 (x^2-y^2)^2 = 0 Also the plot images seem inverted (reflected) along y axis. See plot of the above function in desmos [2]. 1. https://www.2dcurves.com/sextic/sexticsc.html https://www.2dcurves.com/sextic/sexticsc.html 2. https://www.desmos.com/calculator/esrche1qtv https://www.desmos.com/calculator/esrche1qtv
- deleted 6mo ago
  [deleted]
- soupspaces 6mo ago
  See also https://mathcurve.com/courbes2d/scarabee/scarabee.shtml https://mathcurve.com/courbes2d/scarabee/scarabee.shtml

98 points by the-mitr 6mo ago

Related: Wolfram Alpha can generate Pokemon curves: https://www.wolframalpha.com/input?i=pikachu-like+curve https://www.wolframalpha.com/input?i=pikachu-like+curve

sunrunner 6mo ago
I'm getting Mimikyu vibes from it.
soupspaces 6mo ago
Why disjointed if sum of sines?
- smithmayowa 6mo ago
  You're killing me if you don't know the sums of sines could be discontinuous, although this property is usually only apparent when you take the sums of a sine series(e.g Fourier series) to infinity. This particular function is composed of a heaveside step function though which is the reason for its disjointedness.

ktpsns 6mo ago

Beautiful and informative website from the old age: Tables, tiling background pictures, no fancy fonts or colors, even the formulas (equations) are typesetted as low-res bitmaps instead of contemporary MathML/JS/etc. For me, it feels like leafing throught an old vintage book (I have plenty of old math books left from my studies). I find it quite funny that clicking "the author" brings us to Linkedin, feels like going back to reality.

seanhunter 6mo ago

This has got one of my favourite curves in maths, the “Witch of Agnesi” https://www.2dcurves.com/cubic/cubicr.html#witch%20of%20agnesi https://www.2dcurves.com/cubic/cubicr.html#witch%20of%20agne... There are 2 plausible stories about the origin of the name for this curve which was used as an example in a calculus textbook by Maria Agnesi on how to do an integral with partial fractions. The website gives one version of the story, that the curve is named after the latin for a coil of rope which Agnesi then turned into Italian as la versaria. The other possibility is that since the curve was in a problem, she meant l’aversaria (our adversary/opponent, but crucially the feminine version of this noun). In any case, when it was translated into English, the person translating said something along the lines of “Well aversario is the devil, so aversaria must mean ‘witch’” and so the curve became known as the “Witch of Agnesi”. This curve (the folium/leaf of Descartes) is also very cool. https://www.2dcurves.com/cubic/cubicf.html#folium%20of%20Descartes https://www.2dcurves.com/cubic/cubicf.html#folium%20of%20Des... Decartes and Fermat had a massive falling out via letters over trying to get a method of deriving the tangents of this curve, with Decartes insulting Fermat because Fermat’s method was insufficiently rigorous even though Decartes was unable to take the tangent using his method and a modern calculus student would recognize Fermat’s method as very similar to the modern definition of the derivative as the limit of the difference quotient. Decartes was very uncomfortable with the fact that it seemed to be dividing by zero.

lorenzohess 6mo ago

I'm really curious what type of people find a practical use case for this? Graphic designers?

pengaru 6mo ago
seems like an obvious application would be game development? procedural curve functions are used quite a lot, look up "tweening" for instance.
soupspaces 6mo ago
For anyone answering questions like these

ariedro 6mo ago

A glimpse of old times, when the quality of the content mattered more than the presentation.

tobinfricke 6mo ago

Reminds me of the Online Encyclopedia of Integer Sequences https://oeis.org/ https://oeis.org/ But I was somewhat surprised when my first click in this encyclopedia of 2d curves landed me on a 3d sponge https://www.2dcurves.com/3d/3dm.html https://www.2dcurves.com/3d/3dm.html

lioeters 6mo ago

Great collection of curves and articles about them. So many I'd never heard of, I'm enjoying all the pages. The formulae are only in tiny images though, I wish they were in text or MathML. But there's enough information that I can try producing some of my favorite curves and spirals.

leopoldj 6mo ago

There's something wrong with the cartesian equation for scarabaeus [1]. I think it should be: (x^2+y^2) * (x^2+y^2+bx)^2 - a^2 (x^2-y^2)^2 = 0 Also the plot images seem inverted (reflected) along y axis. See plot of the above function in desmos [2]. 1. https://www.2dcurves.com/sextic/sexticsc.html https://www.2dcurves.com/sextic/sexticsc.html 2. https://www.desmos.com/calculator/esrche1qtv https://www.desmos.com/calculator/esrche1qtv

deleted 6mo ago
[deleted]
soupspaces 6mo ago
See also https://mathcurve.com/courbes2d/scarabee/scarabee.shtml https://mathcurve.com/courbes2d/scarabee/scarabee.shtml