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Tartaglia, Cardano and Ferrari – 16th Century Mathematics

64 points by rsj_hn 7y ago

azepoi 7y ago
I can recommand this video on the subject: Mathologer -- 500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle? https://www.youtube.com/watch?v=N-KXStupwsc https://www.youtube.com/watch?v=N-KXStupwsc
- okintheory 7y ago
  As a working applied mathematician, I can tell you it's with pretty good reason. I learnt this stuff in high school and never used it since. It is one of the least useful things you could imagine. It is fun, though.
pdm55 7y ago
One never knows when one might need a particular bit of mathematics. I wrote a mathematical model of DNA transcription events inside E. coli, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5425810/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5425810/. For this, I needed the solution to a cubic equation. Thankfully, Cardano had published the solution in the 15th century, and Wang had shown which was the relevant root in more recent times, https://febs.onlinelibrary.wiley.com/doi/epdf/10.1016/0014-5793%2895%2900062-E https://febs.onlinelibrary.wiley.com/doi/epdf/10.1016/0014-5...
- chongli 7y ago
  Why not use Newton’s method? Your computer is using numerical approximations for computing those roots anyway. The reason the cubic formula isn’t used is because it’s very convoluted and it doesn’t solve any problems you couldn’t solve with Newton’s method, unless you’re doing algebra and you need an exact solution.
  - q_revert 7y ago
    exact analytical solutions are nice as a check against any numerical solutions imo. (checking the same calculations in multiple ways is handy for error catching ime)
blondin 7y ago
first is italian :) hn will bash me for saying but the name reminds me of a pasta brand or name
- sorokod 7y ago
  Not bashing but Tagliatelle (if this is what you are thinking of) is not a brand: https://en.m.wikipedia.org/wiki/Tagliatelle https://en.m.wikipedia.org/wiki/Tagliatelle
- perl4ever 7y ago
  Trivia from googling: Tartaglia comes from tartagliare, meaning to stutter. "Tartaglia was not the family name. Tartaglia took it as a nickname, which referred to his inability to talk clearly as a result of terrible wounds to his head and jaw during the sack of Brescia in 1512" http://galileo.rice.edu/Catalog/NewFiles/tartalia.html http://galileo.rice.edu/Catalog/NewFiles/tartalia.html

64 points by rsj_hn 7y ago

I can recommand this video on the subject: Mathologer -- 500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle? https://www.youtube.com/watch?v=N-KXStupwsc https://www.youtube.com/watch?v=N-KXStupwsc

okintheory 7y ago
As a working applied mathematician, I can tell you it's with pretty good reason. I learnt this stuff in high school and never used it since. It is one of the least useful things you could imagine. It is fun, though.

pdm55 7y ago

One never knows when one might need a particular bit of mathematics. I wrote a mathematical model of DNA transcription events inside E. coli, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5425810/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5425810/. For this, I needed the solution to a cubic equation. Thankfully, Cardano had published the solution in the 15th century, and Wang had shown which was the relevant root in more recent times, https://febs.onlinelibrary.wiley.com/doi/epdf/10.1016/0014-5793%2895%2900062-E https://febs.onlinelibrary.wiley.com/doi/epdf/10.1016/0014-5...

chongli 7y ago
Why not use Newton’s method? Your computer is using numerical approximations for computing those roots anyway. The reason the cubic formula isn’t used is because it’s very convoluted and it doesn’t solve any problems you couldn’t solve with Newton’s method, unless you’re doing algebra and you need an exact solution.
- q_revert 7y ago
  exact analytical solutions are nice as a check against any numerical solutions imo. (checking the same calculations in multiple ways is handy for error catching ime)

blondin 7y ago

first is italian :) hn will bash me for saying but the name reminds me of a pasta brand or name

sorokod 7y ago
Not bashing but Tagliatelle (if this is what you are thinking of) is not a brand: https://en.m.wikipedia.org/wiki/Tagliatelle https://en.m.wikipedia.org/wiki/Tagliatelle
perl4ever 7y ago
Trivia from googling: Tartaglia comes from tartagliare, meaning to stutter. "Tartaglia was not the family name. Tartaglia took it as a nickname, which referred to his inability to talk clearly as a result of terrible wounds to his head and jaw during the sack of Brescia in 1512" http://galileo.rice.edu/Catalog/NewFiles/tartalia.html http://galileo.rice.edu/Catalog/NewFiles/tartalia.html