A couple of weeks ago, I posted an #animation of a point on a circle generating a #cycloid.
If you turn the curve "upside down", you get the #BrachistochroneCurve. This curve provides the shortest travel time starting from one cusp to any other point on the curve for a ball rolling under uniform #gravity. It is always faster than the straight-line travel time.
Anyway, the #animation took a bit of thought as it requires a bit of #Mechanics, some #Integration and is made a bit more tricky as the curve is multi-valued and so you need to treat different branches separately. The #AnimatedGif was produce with #WxMaxima.
[ \sum_{n=0}^{\infty} {\frac{n^4}{n!}}=15e ]
This is strange enough to provoke wonder, but simple enough to serve as an entry-point to an interesting generalization.
English polymath Isaac Newton, who was a mathematician, physicist, astronomer, alchemist, and theologian, died #onthisday in 1727.
His pioneering book Philosophiæ Naturalis Principia Mathematica (1687) consolidated many previous results and established classical mechanics [1]. He also made seminal contributions to optics (among many other things), and shares credit with Gottfried Wilhelm Leibniz for developing calculus.
https://www.youtube.com/watch?v=MwVBzE7Z5gw
Huh maybe if I saw this back in 1st year Uni I wouldn't've failed Calc 1 and would've stayed in the CS program? Could've been a dev. But nah, swapped over to IS&T degree (already met its math req). Kinda was more what I wanted to do anyway though. I still sometimes do wonder. #Integrals#Calculus#Integration
Some things in math will never cease to amaze me no matter how many times I see them. Like Fourier Series: Take a crazy periodic function, and approximate it by a sum of sines and cosines of increasing frequency.
How does a student get to the end of my second-quarter calculus course and still think that [ \frac{1}{x^2+2x+7} = \frac{1}{x^2}+\frac{1}{2x}+\frac{1}{7}, ? ] #algebra#teaching#calculus
I mean, gosh, #calculus dates back to the late seventeenth century. We’ve come a long way but it’s folly to dismiss good material for being of its time and place.
Last Thursday, I gave my first not-small course midterm exam in a long time. It resulted in not the worst-looking exam histogram I've ever created, but pretty far from a happy one. Ugh. #teaching#calculus
I highly recommend “The Continuous, the Discrete, and the Infinitesimal in the Philosophy of Mathematics”, by JL Bell. It has the historical and philosophical views I wanted from his other books, although it does suffer from some of the production errors I mentioned in his other works. Really, he needs a more attentive editor. Nonetheless, the primary and secondary sources are comprehensive, and the sweeping comparative view of different approaches to #calculus and proto-calculus are very productive grounds for deep exploration.
I really like this quote from Berkeley: “…he who can digest a second or third fluxion, a second or third difference, need not, methinks, be squeamish about any point in divinity”
I petition Nabisco to rename “Fig Newtons” to “Fluxions” to so I can digest one or two