History of mathematics · Maths EE idea · Accessible
Completing the square, geometrically
A research question to start from
How did al-Khwarizmi solve quadratic equations geometrically, and how do his cases correspond to the modern quadratic formula?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A historical method reconstructed in diagrams and algebra, then compared.
Mathematics you would need
- Completing the square
- Areas of rectangles and squares
- Negative and zero coefficients
- The quadratic formula
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Reconstruct the geometric method for each case.
- Translate into modern algebra.
- Discuss why there were several cases and what changed with negative numbers.
Scope and difficulty
Accessible. Accessible.
Pitfalls
- History only.
- Cases not explained.
Where to start reading
Search a library catalogue or a university's open lecture notes for: al-Khwarizmi completing the square geometric cases. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).