Champions of Science by Tiner John Hudson

Author:Tiner, John Hudson [Tiner, John Hudson]
Language: eng
Format: epub
Tags: RELIGION / Biblical Biography / General
ISBN: 9781614583097
Publisher: Master Books
Published: 2000-03-01T00:00:00+00:00

Descartes’ circle graph.

For the first time geometrical figures could be replaced with mathematical equations. For instance, a circle could be written as X2 + Y2 = R2, with R the radius of the circle. The radius is the distance from the center out to a point on the circle. The superscript 2 means to square the number; that is, multiply the number by itself. For a circle of radius 5 units, the equation would be X2 + Y2 = 52; that is, X2 + Y2 = 25. Any point on the paper in which the X value and the Y value, when squared and added, equal 25 would be a point on the circle. For instance, the point (3, 4) is on the circle because 32 + 42 = 52; that is, 9 + 16 = 25.

René Descartes’ development of analytical geometry enriched both algebra and geometry. Proving the truth of a mathematical statement using geometry could be long and difficult. Doing the same proof with algebra was usually much easier.

The ancient Greeks and other mathematicians spent time studying conic sections. These curves include the circle, ellipse, parabola, and hyperbola. Cutting a cone at a certain angle makes each one of these figures. Cutting straight across the cone gives a circle and cutting at a slight angle gives an ellipse. Cutting parallel to the side of the cone gives a parabola and cutting parallel to the line down the middle of the cone gives a hyperbola.

A circle is the simplest conic section. Wheels and gears are circular. The circle has the property that every point on the circle is the same distance from its center. The circumference is the distance around the circle. The diameter is a line going from one side of the circle to the other by passing through the center. The ancient Greek scientist Archimedes proved that the number found by dividing the circumference of a circle by its diameter is always a constant. He named this constant pi, a Greek letter. He calculated the value of pi to be about 3 1/7, or as a decimal 3.14.

Pi is the same for any circle, regardless of its size. The distance around a small circle divided by its diameter is the same number as the distance around a large circle divided by its diameter. The division gives the answer 3.14. This is a handy tool for figuring the thickness of circular objects such as trees. With a flexible tape measure, the girth (distance around) a tree is easily measured. Dividing that distance by 3.14 gives the thickness (diameter.) For instance, a tree that is 63 inches around is about 20 inches through the middle (divide 63 by 3.14.)

The ancient Greeks believed the planets traveled in circles. Kepler showed that this was not the case. They traveled in elliptical orbits. The ellipse is another of the conic sections. Looking something like a flattened circle, an ellipse has two points called foci. Going from one focus to a point on the ellipse and back to the other focus is always the same distance.

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