Quadratic, cubic, and quartic...
Transcript of Quadratic, cubic, and quartic...
Quadratic, cubic, and quartic equations
By: David Panson
Quadratic Equations
• Equations with an X2 set to 0
• General formula for the equation is
ax2+bx+c=0
• General Equation for solution is
Cubic Equations • Equations with an X3 set to 0
• General formula for the equation is
ax3+bx2+cx+d=0
Quartic Equations
• Equations with an X4 set to 0
• General formula for the equation is
ax4+bx3+cx2+dx+e=0
The Challenge • Solve with basic operations that cancel and
prevent the use of mind blowing math in a pre calculator era
• Be able to account for negatives and zeros
• Make a uniform way to solve all variations of each problem
Solutions
• Quartic and Cubic
– Roots!
• Quadratic
– Factoring
– Quadratic formula
– Completing the square
Use Today • Math class? And….yeah.
• Quadratic, cubic, and quartic problems are solved still so they most matter right?
• They are needed to understand acceleration of cars, planes, football players, or whatever else, air flow and flight, cell phone signal technology, and tons of other stuff.
• Like math in general they can be found most anywhere. Even hiding in science.
Timeline
• 400 BC Sumerians Start algorithmic thoughts • 300 BC Euclid and his geometry stuff • 600 AD Brahmagupta finds out he can have less than 0 friends (but only
in India.)
• 800 Al Khwarizmi and his 6 class acts • 1145 Savasorda and his best friend. A book. • 1494 Luca Pocioli spreads Suma knowledge • 1515ish Scipione dal Ferro looks at a half full cup. But he thinks its
full.
• 1526 Ferro finally shares his secret… with a stupid genius (Fior)
• 1545 Cardan breaks the bro code. Politely. But Tartaglia is still sad. • 1567 Stifel does a magic trick. Nerd style. • 1637 Descartes makes it FBO… or you know. at least O. • 1673 Leibniz proves that centuries of work is in fact not useless.
Al Khwarizmi’s Classifications of Quadratics
• Squares equal to roots.
• Squares equal to numbers.
• Roots equal to numbers.
• Squares and roots equal to numbers, e.g. x2 + 10x = 39.
• Squares and numbers equal to roots, e.g. x2 + 21 = 10x.
• Roots and numbers equal to squares, e.g. 3x + 4 = x2.
Fior VS Tartaglia
• 30 Problems to be solved in 50 days.
• Fior issued the challenge
• Tartaglia solves all problems super fast(like a boss)
– They were all x3 + mx2 = n form
Timeline for People that aren’t me • 400 BC Sumerians Start algorithmic problem solving • 300 BC Euclid used geometry to answer some quadratics • 600 AD Brahmagupta finds near modern methods but only in India • 800 Al Khwarizmi and indentifies 6 classifications of quadratics. • 1145 Savasorda published Liber Embadorum first published
quadratic method • 1494 Luca Pocioli published Suma unified previous knowledge • 1515ish Scipione dal Ferro solves cubics but only some. • 1526 Ferro finally shares his secret solution with Fior
• 1545 Cardan published Ars Magna and Tartaglias cubic equation • 1567 Stifel condensed previous knowledge into the quadratic
equation • 1637 Descartes published La Giometrie with the modern formula. • 1673 Leibniz proves the equation with a purely algebraic proof.
Works by smarter people • http://www-history.mcs.st-
andrews.ac.uk/HistTopics/Quadratic_etc_equations.html
• http://plus.maths.org/content/101-uses-quadratic-equation-part-ii
• http://dwick.org/pages/cubicquartic.pdf
• http://archives.math.utk.edu/ICTCM/VOL16/C037/paper.pdf
• http://en.wikipedia.org/wiki/Quadratic_equation