Isaac Newton
By: kelston Stephens
Sir issac Newton
• Top Isaac (Sir) Newton (1642-1727) England
• Newton was an industrious lad who built marvelous toys (e.g. a model
windmill powered by a mouse on treadmill). At about age 22, on leave
from University, this genius began revolutionary advances in mathematics,
optics, dynamics, thermodynamics, acoustics and celestial mechanics. He
is most famous for his Three Laws of Motion (inertia, force, reciprocal
action) and Law of Universal Gravitation. As Newton himself
acknowledged, the Laws weren't fully novel: Hipparchus, Ibn al-Haytham,
Galileo and Huygens had all developed much basic mechanics already, and
Newton credits the First Law itself to Aristotle. (However, since Christiaan
Huygens, the other great mechanist of the era and who had also deduced
that Kepler's laws imply inverse-square gravitation, considered the action
at a distance in Newton's universal gravitation to be "absurd," at least this
much of Newton's mechanics must be considered revolutionary. Newton's
other intellectual interests included chemistry, theology, astrology and
alchemy.) Although this list is concerned only with mathematics
motion
•
Although others also developed the techniques independently, Newton is
regarded as the Father of Calculus (which he called "fluxions"); he shares credit
with Leibniz for the Fundamental Theorem of Calculus (that integration and
differentiation are each other's inverse operation). He applied calculus for several
purposes: finding areas, tangents, the lengths of curves and the maxima and
minima of functions. In addition to several other important advances in analytic
geometry, his mathematical works include the Binomial Theorem, his eponymous
numeric method, the idea of polar coordinates, and power series for exponential
and trigonometric functions. (His equation ex = ∑ xk / k! has been called the
"most important series in mathematics.") He contributed to algebra and the
theory of equations, generalizing Déscartes' rule of signs. (The generalized rule of
signs was incomplete and finally resolved two centuries later by Sturm and
Sylvester.) He developed a series for the arcs in function. He developed facts about
cubic equations (just as the "shadows of a cone" yield all quadratic curves, Newton
found a curve whose "shadows" yield all cubic curves). He proved that same-mass
spheres of any radius have equal gravitational attraction: this fact is key to celestial
motions. He discovered Puiseux series almost two centuries before they were reinvented by Puiseux. (Like some of the greatest ancient mathematicians, Newton
took the time to compute an approximation to π; his was better than Vita's,
though still not as accurate as al-Kashi's.)
Newton
• Newton is so famous for his calculus, optics and laws of motion, it is
easy to overlook that he was also one of the greatest geometers.
He solved the Dalian cube-doubling problem. Even before the
invention of the calculus of variations, Newton was doing difficult
work in that field, e.g. his calculation of the "optimal bullet shape."
Among many marvelous theorems, he proved several about
quadrilaterals and their in- or circum-scribing ellipses, and
constructed the parabola defined by four given points. He
anticipated Ponselle's Principle of Continuity. An anecdote often
cited to demonstrate his brilliance is the problem of the
brachistochrone, which had baffled the best mathematicians in
Europe, and came to Newton's attention late in life. He solved it in a
few hours and published the answer anonymously. But on seeing
the solution Jacob Bernoulli immediately exclaimed "I recognize the
lion by his footprint."
1687
• In 1687 Newton published Philosophiae Naturalism Principia
Mathematical, surely the greatest scientific book ever written. The
motion of the planets was not understood before Newton, although
the heliocentric system allowed Kepler to describe the orbits. In
Principia Newton analyzed the consequences of his Laws of Motion
and introduced the Law of Universal Gravitation. (In this work
Newton also proved important theorems about inverse-cube forces,
work largely unappreciated until Chandrasekhar's modern-day
work.) The notion that the Earth rotated about the Sun was
introduced in ancient Greece, but Newton explained why it did, and
the Great Scientific Revolution began. Newton once wrote "Truth is
ever to be found in the simplicity, and not in the multiplicity and
confusion of things." Sir Isaac Newton was buried at Westminster
Abbey in a tomb inscribed "Let mortals rejoice that so great an
ornament to the human race has existed