Why Is Math So Fascinating?

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The discussion revolves around sharing fascinating mathematical concepts and experiences that can impress others. Key highlights include the significance of the number "e" in growth calculations, particularly its relationship to exponential functions and natural logarithms. Participants express awe over Euler's identity, which connects e, π, and i in a surprising way, and share personal revelations about mathematical principles, such as the Cantor set and the implications of infinity. The conversation also touches on brain teasers, like the string around the Earth problem, which illustrates surprising mathematical truths, and the beauty of graphical representations of complex numbers. Participants recount moments of enlightenment in their mathematical journeys, emphasizing the depth and interconnectedness of mathematical concepts, including calculus, linear algebra, and topology. The discussion reflects a shared appreciation for the elegance and complexity of mathematics, highlighting how these revelations can reshape one's understanding of the subject.
  • #61
Do you have a friend in the printing business? I floated a calendar project to a couple of locals, who acted quite underwhelmed.
 
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  • #62
turbo-1 said:
That is the "magic". You get to apply symmetries, inversions, etc to make your images. Most of the horsepower comes from choosing which functions you want to apply in each layer, where to set the transparency limits and how to implement those, and what color schemes and gradients to apply. You can of course recover Mandelbrot and Julia sets in their original iterations and make beautiful images playing with only palettes and gradation slopes, etc, but that is not really satisfying. As I noted in another post recently, my "take" on creativity has a decidedly technical bent.
Not wishing to cast aspersions upon these quite beautful works, but it seems to me, the real charm of Mandelbrot set and Julia sets is that they are entirely natural. This seems like the gilding of a pretty incredible lily.
 
  • #63
I still am amazed at how the ratio of pi was discovered. And how people just purely invented mathematical focuses, like calculus. It would be amazing to be that brilliant...
 
  • #64
the series sum 1/1^2 + 1/2^2 + 1/3^2 + ... is amazing, i think it equals pi^2/6, and was calculated by euler in his precalculus book.
 

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