500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle?

Why is it that, unlike with the quadratic formula, nobody teaches the cubic formula? After all, they do lots of polynomial torturing in schools and the discovery of the cubic formula is considered to be one of the milestones in the history of mathematics. It's all a bit of a mystery and our mission today is to break through this mathematical wall of silence! Lots of cubic (and at the very end quartic) surprises ahead.

A great starting point for further exploration of this topic is this wiki page:

https://en.wikipedia.org/wiki/Cubic_function

Closest to what I do in this video is this paper

A New Approach to Solving the Cubic: Cardan's Solution Revealed Author(s): R. W. D. Nickalls, The Mathematical Gazette, Vol. 77, No. 480 (Nov., 1993), pp. 354-359

Here is a writeup of the great feud Tartaglia v. Cardano (minus all the made up bits).

https://arxiv.org/abs/1308.2181

Tartaglia's poem

https://www.maa.org/press/periodicals/convergence/how-tartaglia-solved-the-cubic-equation-tartaglias-poem

Here is a writeup of a way of solving the cube by completing the cube (not so easy to motivate as what I've got in the video):

http://mathforum.org/dr.math/faq/faq.cubic.equations2.html

Fun fact 1:
https://en.wikipedia.org/wiki/Cubic_function#Collinearities

Fun fact 2:
https://en.wikipedia.org/wiki/Cubic_function#Three_real_roots

Fun fact 3 (Marden's theorem)
https://www.maa.org/press/periodicals/loci/joma/the-most-marvelous-theorem-in-mathematics

Extra Superman commented: At 3:12, the cubic equation that you choose is in one of two infinite families.The first one: for odd n, x^3 - 3nx - (n^3+1). The second one: for odd n, x^3 + 3nx - (n^3-1).

Thank you very much to Marty for all his help with polishing the presentation and Andrea for his help with pronouncing all those Italian words.

Enjoy :)

P.S. For some places that sell the t-shirts that I am wearing today google "cube root t-shirt" and "square root t-shirt"
The music is Morning Mandolin by Chris Haugen https://youtu.be/i8fH6la-bJQ from the free YouTube audio library

Two ways to support Mathologer
Mathologer Patreon: https://www.patreon.com/mathologer
Mathologer PayPal: paypal.me/mathologer
(see the Patreon page for details)

Видео 500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle? канала Mathologer