John Wallis (1616-1703)
INTRODUCING OUR NEW PRODUCTS
He joined a secret group of scientists that evolved into what is known as the Royal Society.
There, he was able to explore his mathematical interests and began writing his own treatise.
Contributions to: 1. trigonometry 2. calculus 3. geometry 4. analysis of infinite series.
Contributed to Analytic Geometry, Integral Calculus, Collision of bodies, and Algebra
*Credited with the proof of the Pythagorean Theorum using similar triangles
1655: Treatise on the Conic Sections
described the curves that are obtained as cross sections
Popularized the infinity symbol in his treatise
laid down the principal of interpolation
Arithmetica Infinitorum, 1656
developed the standard notation for powers
by integration, found the area enclosed between the curve y = x^m, the axis of x, and any ordinate x = h
Integral Calculus Cont.
oEstablished the formula: ½ = (184.108.40.206.220.127.116.11.10..) / (18.104.22.168.22.214.171.124.9...) oDiscussed formation and properties of continued fractions o1659: solution of the problems on the cycloid which had been proposed by Blaise Pascal. oHe extended the methods of Descartes and Cavalieri.
THE THEORY: -proposed by the Royal Society in 1668 -utilized what is now called the conservation of momentum -inelastic vs elastic collisions
Collision of Bodies
-Published Algebra, 1685, and a second addition Opera, 1693 -First systematic use of formulas -Accepts negative and complex roots -He also criticizes Descartes' Rule of Signs stating that it is only valid if all the roots of the equation are real.