Updated 2004-04-06

Cubic equations
This work deals with the evolution of  different methods of
treating the "cubic" from  both mathematical and historical
point of view. The history of finding roots of polynomials goes 
a long way back, a lot is written about the early mathematics
but we do not find any advanced steps until we reach the
mathematics of the Babylonians and the Egyptians of 
about 3000 BC.

1. Introduction, where (and some thoughts about why) the first steps were taken.
2. Four problems of antiquity
3. Basics about what a cubic equation is, and how to find its solution.
4. Cubics in Babylonia about 2000BC.
5. Cubics in China around 100 BC to 1000 AD
6. Cubics in India 500BC- .
7. Cubics in Greece, around 300 BC - .
8. Cubics in the Arabic world, 700- 1100 AD.
9. Fibonacci and his approximate solution to x³ + 2x² +10x =20. 
10. Gerard and his attempt, 1300 AD.
11. dal Ferro who solved ax³ + bx = c sometimes between 1500 and 1515
12. Similarities between the solution of second degree and the cubic equation
13. Fior inherited dal Ferros solution.
14. Challenged by Fior, Tartaglia found the complete solution, around 1530.
15. Cardano published the dal Ferro/Tartaglia solution in 1545.
16. Bombellis work with imaginary numbers 1569.
17. Cardanos geometrical solution
18. Geometrical properties
19. After the discovery of the general solutions
20. Galois and the cubic equation
21. An entirely different approach by  Kalman/White
22. Completing the cube
23. The hyperbolic solution
24. Solving some special cubic equations
25. Solve your own cubic using a JAVA-script
26. Graphing polynomials of higher degree
27. Some exercises
28. Summary
29. References

Biographies: Omar Khayyam, Scipione dal Ferro, Antonio Maria Fior,. Niccolo Tartaglia, 34. Girolamo Cardano

(More is coming  - about the mathematics  in the places where the development started) 35. Arabic world 36. Egypt 37. Greece 38. India

Carsten Magnusson carsten.magnusson@jll.se