Conics consists of eight different books but only seven still survive. The first four have survived in the original Greek but there is an Arabic translation of seven of the eight books. Apollonius wrote the book at the request of Naucrates, another mathematician who had visited him in Alexandria. Apollonius had to finish the book quickly because Naucrates was leaving Alexandria. After writing the book and giving it to Naucrates, Apollonius spent more time on the book and revised some of the material.
The revised edition is what make up the book. The definition of a conic states that it is the curve one gets at the intersection of a cone and a plane.
By changing the place and angle of the intersection, different conic sections are created. This basically just means that you can cut a cone in a specific angle to get different curves.
To some extent, the first four books utilize the work of other mathematicians although Apollonius claims that he was expanded on the work and developed the work more than previous writers.
Most of the material would be well known to them. Book one looks at conics and their properties. He develops ways to create the three conics or sections, which he identifies as parabola, ellipse, and hyperbola.
He then describes the three sections. Apollonius also looks at the basic properties of these three sections. Apollonius states that he has developed the concepts to a higher degree than previous writers. Book two looks at diameters and axes of the conic sections as well as asymptotes. An axis is simply a straight line the cuts an object into two. An asymptote is a straight line that comes close to a curve but does not meet it.
Book three contains some original material and does not simply restate the work of other mathematicians. Apollonius states that he discovered new ideas on how to create solid loci a locus is another conic section. He writes that after he came up with some of these ideas, he realized that Euclid had not figured out how to create locus using three and four lines. Apollonius stated that this was impossible to do without using the theorems that he had discovered.
Apollonius also dealt with focal properties and with rectangles found in conic segments. Book four looks at the different ways that conic sections or the circumference of a circle can meet each other. Apollonius states that a lot of the material in book four has not been addressed by other mathematicians. The first four books are a result of Apollonius organizing the work of other mathematicians into a more organized whole. Previously, this work was a set of various theorems that were not connected in any way.
Apollonius was a good enough mathematician to see how the various theorems could be connected according to his general method. Since , the English Wikipedia page of Apollonius of Perga has received more than , page views. His biography is available in 59 different languages on Wikipedia up from 57 in Apollonius of Perga is the 44th most popular mathematician , the th most popular biography from Turkey up from th in and the 2nd most popular Turkish Mathematician.
Apollonius of Perga is most famous for his work on conic sections. He is also credited with inventing the terms "parabola," "ellipse," and "hyperbola. Among mathematicians, Apollonius of Perga ranks 44 out of The two easiest involve three points or three straight lines and were first solved by Euclid. Solutions to the eight other cases, with the exception of the three-circle problem, appeared in Tangencies ; however, this work was lost. Any of the eight circles that is a solution to the general three-circle problem is called an Apollonius circle.
If the three circles are mutually tangent then the eight solutions collapse to just two, which are known as Soddy circles. If, having started with three mutually tangent circles and having created a fourth — the inner Soddy circle — that is nested between the original three, the process is repeated to yield three more circles nested between sets of three of these, and then repeated again indefinitely, fractal is produced.
The points that are never inside a circle form a fractal set called the Apollonian gasket , which has a fractional dimension of about 1. Apollonius of Perga c. Apollonius problem The Apollonius problem is: given three objects in the plane , each of which may be a circle C , a point P a degenerate circle , or a line L part of a circle with infinite radius , find another circle that is tangent to just touches each of the three.
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