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.
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:
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.
> 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
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:
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.
