
The Birth of Calculus (1986) [video] - gauthamshankar
https://www.youtube.com/watch?v=ObPg3ki9GOI
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Strilanc
The really interesting thing about this video, to me, is the explanation of
how tangents were calculated _before_ calculus. You can see how awkward it
would have been to do things that way, and how it would have been difficult to
realize they was something far far easier.

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29athrowaway
Trigonometric functions have existed for a long time. And in the past, more
trigonometric functions were used:

\- versed sine (versin) and versed cosine (vercos)

\- coversed sine (coversin) and coversed cosine (covercos)

\- haversed sine (haversin) and haversed cosine (havercos)

\- hacoversed sine (hacoversin) and hacoversed cosine (hacovercos)

\- exsecant and excosecant

Perhaps I am forgetting some. Many alternative mnemonics exist for these too.

This formula was very important:
[https://en.wikipedia.org/wiki/Haversine_formula](https://en.wikipedia.org/wiki/Haversine_formula)

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acqq
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 work on his calculating machine:

[https://en.wikipedia.org/wiki/Stepped_reckoner](https://en.wikipedia.org/wiki/Stepped_reckoner)

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beervirus
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.

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29athrowaway
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...](https://fliptomato.wordpress.com/2007/03/19/medical-researcher-
discovers-integration-gets-75-citations/)

~~~
lqet
OP is not joking, the original paper is available here:

[https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf](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
> formulas. The total sum of these individual areas thus represents the total
> area under the curve

~~~
olooney
Is this not just the trapezoidal rule for numeric integration?

[https://en.wikipedia.org/wiki/Trapezoidal_rule](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](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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Vysero
The difference between Newton and Leibniz seems remarkably similar to the
difference between say: Einstein and Feynman. One seems to be discovering the
maths while the other seems to be forging it. Personally, I prefer and
understand the forged methodology better myself, but then again I have always
been a tinkerer.

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z991
Transcript:
[https://youtubetranscript.com/?v=ObPg3ki9GOI](https://youtubetranscript.com/?v=ObPg3ki9GOI)

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melling
Are the original notebooks online?

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laichzeit0
I've seen Newton's notebooks online before.

