By John Tabak
Illustrates the altering courting among arithmetic and nature from the early makes an attempt of mathematicians to use deductive reasoning to nature to the upheaval triggered at the present time via the invention of such normal phenomena as surprise waves.
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Additional info for Mathematics and the Laws of Nature: Developing the Language of Science (The History of Mathematics)
Over time they developed multiple mathematical systems for predicting the positions of astronomical objects. These systems required the user to know a small number of facts about the object of interest and be able to solve certain algebraic equations. No longer did these early astronomers require generations of record keepers because they no longer depended so heavily on past observations. To understand what they did and the difficulties that they overcame, we examine their method of predicting the position of the Sun along the ecliptic.
Every line that is perpendicular to Earth’s surface points at Earth’s center so l1 and l2 intersect at Earth’s center. • There is a third line to take into account. This is the line determined by the ray of sunlight that strikes the end of the stick. Call this line l3. Because Eratosthenes assumed that rays of light from the Sun are parallel, l1 and l3 are parallel, and l2, the line determined by the stick, forms two equal acute (less than 90°) angles, where it crosses l1 and l3. • Of course Eratosthenes could not see the angle formed at Earth’s center, but he knew how to use the height of the stick and the length of the shadow cast by the stick to compute the angle formed at the tip of the stick by the Sun’s ray, l3, and the stick itself, l2.
Now acknowledged as much more elementary than that of Archimedes, exerted a far greater influence on the history of science and mathematics than anything that Archimedes wrote. One reason is that Archimedes’ writing style is generally harder to read than the writings of many of his contemporaries. It is terser; he generally provides less in the way of supporting work. Archimedes requires more from the reader even when he is solving a simple problem. But it is more than a matter of style. The problems that he solves are generally harder than those of most of his contemporaries.
Mathematics and the Laws of Nature: Developing the Language of Science (The History of Mathematics) by John Tabak