The Birth of Calculus (1986) [video]
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The Birth of Calculus (1986) [video]
1–10 of 13 posts
Re: The Birth of Calculus (1986) [video]
#2The 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.
Re: The Birth of Calculus (1986) [video]
#3People 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...
Re: The Birth of Calculus (1986) [video]
#4Wonderful. 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:
Re: The Birth of Calculus (1986) [video]
#5Transcript: https://youtubetranscript.com/?v=ObPg3ki9GOI
Re: The Birth of Calculus (1986) [video]
#6Are the original notebooks online?
Re: The Birth of Calculus (1986) [video]
#7The 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.
Re: The Birth of Calculus (1986) [video]
#8People 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 formulas. The total sum of these individual areas thus represents the total area under the curve
Re: The Birth of Calculus (1986) [video]
#9People 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…
Tai's "integration" method also has references to previous, similar work, and has 293 citations. You can buy the paper for $35.
Academia in a nutshell.
Re: The Birth of Calculus (1986) [video]
#10The 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.
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