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The Birth of Calculus (1986) [video]

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Re: The Birth of Calculus (1986) [video]

#11

Post by beervirus »

acqq wrote: post #4

Wonderful. Some very interesting and very precise historical details. I can only be sad to imagine how something on that subject would be produced today (with so much sound and visual effects and removing the substance to be practically unwatchable). They just don't make them like that anymore, sadly. Also good to be remembered that a lot of work of Leibniz was in some way inspired or motivated by, or related to his…

There's some math content on youtube that's great, and wouldn't have been possible 30-odd years ago. I'm mostly thinking of 3blue1brown, but I'm sure there are other examples.

Re: The Birth of Calculus (1986) [video]

#12

Post by olooney »

lqet wrote: post #8
29athrowaway wrote: post #3

People often know about Isaac Newton but not Isaac Barrow. Or the greatest of all, the doctor that rediscovered integration in 1994. https://fliptomato.wordpress.com/2007/03/19/medical-research...

OP is not joking, the original paper is available here: https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf > RESEARCH DESIGN AND METHODS— In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical for…

Is this not just the trapezoidal rule for numeric integration?

https://en.wikipedia.org/wiki/Trapezoidal_rule

It's not even a particular good choice for the specific problem (glucose curve) because the trapezoidal rule will systematically underestimate the true area when the curvature is always negative. Simpson's rule is almost always a better choice:

https://en.wikipedia.org/wiki/Simpson%27s_rule

Fun fact: although the method is attributed to the 18th century mathematician Simpson, Kepler is known to have used it in the 17th century.

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