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> The great mathematician Aryabhata (476-550), in his masterwork composed when he was only 23, covers square and cube roots, the properties of circles and trian

> The great mathematician Aryabhata (476-550), in his masterwork composed when he was only 23, covers square and cube roots, the properties of circles and triangles, algebra, quadratic equations and sines, and contains a decent approximation of the value of pi at 3.1416. TIL...

canfakt 2y ago
The man was certified genius, here are some more of his contributions to the world - Invention of Zero - Decimal Place-Value System - Astronomical Calculations - Understanding of Negative Numbers here is a good YouTube video on this subject https://www.youtube.com/watch?v=jgjcy04PDRM https://www.youtube.com/watch?v=jgjcy04PDRM While we praise Aryabhatta man, i would like to shed some lights on Madhava of Sangamagrama c. 1340 - c. 1425 CE from India who less well known Key Contributions Infinite Series and Trigonometry Discovered power series expansions for trigonometric functions: Madhava's Sine Series: Infinite series representation for the sine function. Madhava's Cosine Series: Infinite series representation for the cosine function. Madhava–Gregory Series: Series for the arctangent function, predating James Gregory by over 200 years. Calculus and Mathematical Analysis Laid early foundations of calculus through: 200 years before Newton or leibniz Methods of term-by-term integration and iterative techniques for solving transcendental equations. Concepts related to the area under curves, similar to integral calculus. Introduction of convergence tests for infinite series. Creation of trigonometric tables with accurate sine and cosine values. The Jesuit missionaries in India played a crucial role in the transmission of advanced Indian mathematical and astronomical knowledge to Europe by learning local languages, collaborating with local scholars, and documenting key works, thereby significantly influencing the development of mathematics in the West.
fuzztester 2y ago
>contains a decent approximation of the value of pi at 3.1416. I read this somewhere earlier, in some article about the history of mathematics, maybe Indian, Chinese, or both: Take the number 113355 (easy to remember). Split it down the middle to get 113 and 355. Divide the latter by the former. E.g. in the Python shell: > print (355/113) Result: 3.1415929203539825 which is a slightly closer approximation to pi than 3.1416.
- pablobaz 2y ago
  That's nice! Another one is remembering the phrase: Can I have a large container of coffee please sir.
  - deleted 2y ago
    [deleted]
  - fuzztester 2y ago
    That's nicer! TIL. :) Googled it. Here is a result that explains it, since some of the others seem vague: https://www.reddit.com/r/todayilearned/comments/l6icp/til_you_can_remember_the_value_of_pi_31415926_by/ https://www.reddit.com/r/todayilearned/comments/l6icp/til_yo...
  - kanamekun 2y ago
    But please has 6 letters?
    - I_complete_me 2y ago
      Check this one: "Now I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics"
      - fuzztester 2y ago
        head = spin. from early pg essay. :) now i need to write a python program to count the letters in the words and map them to pi's official digits, to check your 'formula'. ;) easy as pi.
fuzztester 2y ago
https://en.m.wikipedia.org/wiki/List_of_Indian_mathematicians https://en.m.wikipedia.org/wiki/List_of_Indian_mathematician...
defrost 2y ago
The same kind of math found on Babylonian clay tablets from 2,000 years earlier then? https://en.wikipedia.org/wiki/Babylonian_mathematics https://en.wikipedia.org/wiki/Babylonian_mathematics Which suggests a long oral and|or easily destroyed "document" tradition of teachings being passed down which came to Aryabhata who compiled such things in a manner that survived. https://en.wikipedia.org/wiki/Babylonian_mathematics https://en.wikipedia.org/wiki/Babylonian_mathematics
- srean 2y ago
  The sophistication of Babylonian mathematics boggles my mind. I am sure a credible science fiction story could be told where the Babylonians are a sophisticated alien race making Earth their home. However, "the same kind of mathematics" rings dismissive. Trigonometry as we know it, came to its own and flourished in the middle ages in Indian, Arab and Persian civilizations. I am not aware of Babylonic trigonometry. The story of the name of sin is itself quite interesting. It was half a 'jyay' (meaning chord subtended by an angle) in India. Through transliteration it became 'jayb' to the Arabs. Or the Europeans who were translating the Arabic mathematical literature derived from India, transliterate it as 'jayb', a phonetically similar bonafide Arabic word, that to this day is used to mean, a pocket/wallet/cavity. So pocket becomes sinus in Latin and then it evolves into just 'sin'. I think it was Napier who gave the name that we use. Cultivation of geometry by Indian scholars go further in the past, to about 8th century BC as recorded in Sulbasutra. https://personal.math.ubc.ca/~cass/courses/m309-01a/kong/sulbasutra_geometry.htm https://personal.math.ubc.ca/~cass/courses/m309-01a/kong/sul... You might be interested to know that combinatorics was also a hot topic among the Indian mathematicians. What we know as Fibonacci goes back far in the past, to Pingala (250 BC +/- 50). Pingala had worked out the binary numeral system and the 'Fibonacci' series. https://en.wikipedia.org/wiki/Pingala https://en.wikipedia.org/wiki/Pingala What I am really keen to know is the mathematics of the Indus valley civilization, they were contemporaries of the Babylonians. Scarce little is known about their mathematics.
  - defrost 2y ago
    > However, "the same kind of mathematics" rings dismissive. That's on you if you read it that way; There are other sources, but sticking with the wikipedia article already linked (which references other sources): * The Babylonian astronomers kept detailed records of the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere. "angular distances measured on spheres" is the domain of trigonometry, how deep is a matter of debate but trigonometry it is. * They also used a form of Fourier analysis to compute an ephemeris (table of astronomical positions), which was discovered in the 1950s by Otto Neugebauer. That seems reasonably advanced. * Tablets kept in the British Museum provide evidence that the Babylonians even went so far as to have a concept of objects in an abstract mathematical space. The tablets date from between 350 and 50 B.C.E., revealing that the Babylonians understood and used geometry even earlier than previously thought. The Babylonians used a method for estimating the area under a curve by drawing a trapezoid underneath, a technique previously believed to have originated in 14th century Europe. This is proto-integration, pre-caclulus, etc.

canfakt 2y ago

The man was certified genius, here are some more of his contributions to the world - Invention of Zero - Decimal Place-Value System - Astronomical Calculations - Understanding of Negative Numbers here is a good YouTube video on this subject https://www.youtube.com/watch?v=jgjcy04PDRM https://www.youtube.com/watch?v=jgjcy04PDRM While we praise Aryabhatta man, i would like to shed some lights on Madhava of Sangamagrama c. 1340 - c. 1425 CE from India who less well known Key Contributions Infinite Series and Trigonometry Discovered power series expansions for trigonometric functions: Madhava's Sine Series: Infinite series representation for the sine function. Madhava's Cosine Series: Infinite series representation for the cosine function. Madhava–Gregory Series: Series for the arctangent function, predating James Gregory by over 200 years. Calculus and Mathematical Analysis Laid early foundations of calculus through: 200 years before Newton or leibniz Methods of term-by-term integration and iterative techniques for solving transcendental equations. Concepts related to the area under curves, similar to integral calculus. Introduction of convergence tests for infinite series. Creation of trigonometric tables with accurate sine and cosine values. The Jesuit missionaries in India played a crucial role in the transmission of advanced Indian mathematical and astronomical knowledge to Europe by learning local languages, collaborating with local scholars, and documenting key works, thereby significantly influencing the development of mathematics in the West.

fuzztester 2y ago

>contains a decent approximation of the value of pi at 3.1416. I read this somewhere earlier, in some article about the history of mathematics, maybe Indian, Chinese, or both: Take the number 113355 (easy to remember). Split it down the middle to get 113 and 355. Divide the latter by the former. E.g. in the Python shell: > print (355/113) Result: 3.1415929203539825 which is a slightly closer approximation to pi than 3.1416.

pablobaz 2y ago
That's nice! Another one is remembering the phrase: Can I have a large container of coffee please sir.
- deleted 2y ago
  [deleted]
- fuzztester 2y ago
  That's nicer! TIL. :) Googled it. Here is a result that explains it, since some of the others seem vague: https://www.reddit.com/r/todayilearned/comments/l6icp/til_you_can_remember_the_value_of_pi_31415926_by/ https://www.reddit.com/r/todayilearned/comments/l6icp/til_yo...
- kanamekun 2y ago
  But please has 6 letters?
  - I_complete_me 2y ago
    Check this one: "Now I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics"
    - fuzztester 2y ago
      head = spin. from early pg essay. :) now i need to write a python program to count the letters in the words and map them to pi's official digits, to check your 'formula'. ;) easy as pi.

fuzztester 2y ago

https://en.m.wikipedia.org/wiki/List_of_Indian_mathematicians https://en.m.wikipedia.org/wiki/List_of_Indian_mathematician...

defrost 2y ago

The same kind of math found on Babylonian clay tablets from 2,000 years earlier then? https://en.wikipedia.org/wiki/Babylonian_mathematics https://en.wikipedia.org/wiki/Babylonian_mathematics Which suggests a long oral and|or easily destroyed "document" tradition of teachings being passed down which came to Aryabhata who compiled such things in a manner that survived. https://en.wikipedia.org/wiki/Babylonian_mathematics https://en.wikipedia.org/wiki/Babylonian_mathematics

srean 2y ago
The sophistication of Babylonian mathematics boggles my mind. I am sure a credible science fiction story could be told where the Babylonians are a sophisticated alien race making Earth their home. However, "the same kind of mathematics" rings dismissive. Trigonometry as we know it, came to its own and flourished in the middle ages in Indian, Arab and Persian civilizations. I am not aware of Babylonic trigonometry. The story of the name of sin is itself quite interesting. It was half a 'jyay' (meaning chord subtended by an angle) in India. Through transliteration it became 'jayb' to the Arabs. Or the Europeans who were translating the Arabic mathematical literature derived from India, transliterate it as 'jayb', a phonetically similar bonafide Arabic word, that to this day is used to mean, a pocket/wallet/cavity. So pocket becomes sinus in Latin and then it evolves into just 'sin'. I think it was Napier who gave the name that we use. Cultivation of geometry by Indian scholars go further in the past, to about 8th century BC as recorded in Sulbasutra. https://personal.math.ubc.ca/~cass/courses/m309-01a/kong/sulbasutra_geometry.htm https://personal.math.ubc.ca/~cass/courses/m309-01a/kong/sul... You might be interested to know that combinatorics was also a hot topic among the Indian mathematicians. What we know as Fibonacci goes back far in the past, to Pingala (250 BC +/- 50). Pingala had worked out the binary numeral system and the 'Fibonacci' series. https://en.wikipedia.org/wiki/Pingala https://en.wikipedia.org/wiki/Pingala What I am really keen to know is the mathematics of the Indus valley civilization, they were contemporaries of the Babylonians. Scarce little is known about their mathematics.
- defrost 2y ago
  > However, "the same kind of mathematics" rings dismissive. That's on you if you read it that way; There are other sources, but sticking with the wikipedia article already linked (which references other sources): * The Babylonian astronomers kept detailed records of the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere. "angular distances measured on spheres" is the domain of trigonometry, how deep is a matter of debate but trigonometry it is. * They also used a form of Fourier analysis to compute an ephemeris (table of astronomical positions), which was discovered in the 1950s by Otto Neugebauer. That seems reasonably advanced. * Tablets kept in the British Museum provide evidence that the Babylonians even went so far as to have a concept of objects in an abstract mathematical space. The tablets date from between 350 and 50 B.C.E., revealing that the Babylonians understood and used geometry even earlier than previously thought. The Babylonians used a method for estimating the area under a curve by drawing a trapezoid underneath, a technique previously believed to have originated in 14th century Europe. This is proto-integration, pre-caclulus, etc.