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Jones introduces the Greek letter π to represent the ratio of the circumference of a circle to its diameter in his Synopsis palmariorum matheseos (A New Introduction to Mathematics).
Newton publishes Arithmetica universalis (General Arithmetic) which contains a collection of his results in algebra.
De Moivre uses trigonometric functions to represent complex numbers in the form r(cos x + i sin x).
La Hire calculates the length of the cardioid. (See this Famous curve.)
Arbuthnot publishes an important statistics paper in the Royal Society which discusses the slight excess of male births over female births. This paper is the first application of probability to social statistics.
Giovanni Ceva publishes De Re Nummeraria (Concerning Money Matters) which is one of the first works in mathematical economics.
Jacob Bernoulli's book Ars conjectandi (The Art of Conjecture) is an important work on probability. It contains the Bernoulli numbers which appear in a discussion of the exponential series.
Brook Taylor publishes Methodus incrementorum directa et inversa (Direct and Indirect Methods of Incrementation), an important contribution to the calculus. The book discusses singular solutions to differential equations, a change of variables formula, and a way of relating the derivative of a function to the derivative of the inverse function. There is also a discussion on vibrating strings.
Johann Bernoulli declares that the principle of virtual displacement is applicable to all cases of equilibrium.
Jacob Bernoulli's work on the calculus of variations is published after his death.
De Moivre publishes The Doctrine of Chances. The definition of statistical independence appears in this book together with many problems with dice and other games. He also investigated mortality statistics and the foundation of the theory of annuities.
Brook Taylor publishes New principles of linear perspective. The first edition appeared four years earlier under the title Linear perspective. The work gives the first general treatment of vanishing points.
List of mathematicians alive in 1720.
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JOC/EFR August 2001
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