Quadratic Roots The Carlyle Circle Ed Staples CMA
- Slides: 80
Quadratic Roots & The Carlyle Circle Ed Staples CMA 17 August 2019
Tschirnhaus Transformation
Quadratic formula
The Tschirnhaus transformation
The Tschirnhaus transformation
Simple in application
Simple in application
Simple in application
Simple in application
Simple in application
Simple in application
Simple in application
A Tschirnhaus transformation
Task 1
Task 1
Task 1
Task 1
Task 1
Task 1
Task 1
Task 1
Compare with Cubic transformation
Compare with Cubic transformation
The cubic solution first steps
The cubic solution first steps
The cubic solution first steps
Original cubic
…divide by a
Tschirnhaus transformation x=y+5
Solutions by Descartes
Descartes: 1 st Type
An example to follow
Why it works…
Check by completing squares
Task 2
Task 2
Task 2
Task 2
Task 2
Task 2
Draw in the red oblique line
Descartes: 2 nd Type
An example to follow
Why it works…
Check by completing squares
Task 3
Task 3
Task 3
Task 3
Task 3
Task 3
Draw in the red vertical line
The Carlyle Circle Scottish Philosopher Satirical writer Essayist Translator Historian Mathematician Teacher
The Carlyle Circle It was very good of God to let Carlyle and Mrs. Carlyle marry one another…. And so make only two people miserable and not four! Samuel Butler Scottish Philosopher Satirical writer Essayist Translator Historian Mathematician Teacher
Portrait by Helen Allingham 1879
Craigenputtock House, Scotland
E. J. Hornsby: Geometrical and Graphical solutions of Quadratic Equations Thomas Carlyle (1795 -1881) Carlyle’s method first appeared in the popular: Elements of Geometry by Sir John Leslie (1766 – 1832) The solution of this important problem…. …. was suggested to me by Mr. Thomas Carlyle …an ingenious young mathematician, and formerly my pupil.
The problem
Possible motivation
Possible motivation
Possible motivation r, s
The general method
An example
Equation of Circle
Warning
Task 4
Steps
Steps
Steps
Steps
Steps
Steps
Descartes and Carlyle
More things to think about • Lill’s method of finding roots https: //www. mathematicalwhetstones. com/blog
More things to think about • Send in a project to the CMA committee!