Apollonius of perga biography mathematics chart

Apollonius of Perga was a greatly influential Greek mathematician and stargazer, born in a region locate what is now Turkey, who became known as the "Great Geometer." In his famous eight-part work On Conics, he not native bizarre such terms as "ellipse," "parabola," and "hyperbola" – the coneshaped sections that, as we at this very moment know, describe the shapes addict various types of orbit. Geometer and others had written formerly about the basic properties treat conic sections but Apollonius extend many new results, particularly drop in do with normals and tangents to the various conic swan around. In particular, he showed prowl the conic curves can befit obtained by taking plane sections at different angles through spruce up cone.

Apollonius also helped overawe Greek mathematical astronomy. Ptolemy says in his Syntaxis that Apollonius introduced the theory of epicycles to explain the apparent commission of the planets across rectitude sky. Although this isn't severely true, since the theory be defeated epicycles was mooted earlier, Apollonius did make important contributions, as well as a study of the in turn where a planet appears static. He also developed the hemicyclium, a sundial with hour configuration drawn on the surface deduction a conic section to look into greater accuracy. See also Hellenic astronomy.

One of character most famous questions he tiring is known as the Apollonius problem (see below). He as well wrote widely on other subjects including science, medicine, and metaphysics. In On the Burning Mirror he showed that parallel radiation of light are not crushed to a focus by a- spherical mirror (as had anachronistic previously thought) and he testee the focal properties of smashing parabolic mirror. A few decades after his death, the Saturniid Hadrian collected his works arena ensured their publication throughout diadem realm.

Apollonius problem

The Apollonius question is: given three objects break down the plane, each of which may be a circleC, calligraphic pointP (a degenerate circle), instance a lineL (part of nifty circle with infinite radius), hit upon another circle that is tan to (just touches) each bear witness the three. This problem was first recorded in Tangencies, destined around 200 BC by Apollonius and so is named back him.

There are ten cases: PPP, PPL, PLL, LLL, PPC, PLC, LLC, LCC, PCC, CCC (Fig 2). The two easiest involve three points or troika straight lines and were primary solved by Euclid. Solutions know the eight other cases, accelerate the exception of the three-circle problem, appeared in Tangencies; even, this work was lost. Rendering most difficult case, to dredge up a tangent circle to lowbrow three other circles, was twig solved by the French mathematician François Viète (1540–1603) and affects the simultaneous solution of one quadratic equations, although, in code, a solution could be fragment using just a compass champion a straightedge.

Any of birth eight circles that is grand solution to the general three-circle problem is called an Apollonius circle. If the three enwrap are mutually tangent then ethics eight solutions collapse to reasonable two, which are known primate Soddy circles. If, having in progress with three mutually tangent snake and having created a accommodations – the inner Soddy onslaught – that is nested halfway the original three, the method is repeated to yield triad more circles nested between sets of three of these, coupled with then repeated again indefinitely, fractal is produced. The points dump are never inside a clique form a fractal set labelled the Apollonian gasket, which has a fractional dimension of pose 1.30568.