# plane+figure

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**Problem of Apollonius**— In Euclidean plane geometry, Apollonius problem is to construct circles that are tangent to three given circles in a plane (Figure 1); two circles are tangent if they touch at a single point. Apollonius of Perga (ca. 262 BC ndash; ca. 190 BC)… …82

**Mohr's circle**— Mohr s circles for a three dimensional state of stress Mohr s circle, named after Christian Otto Mohr, is a two dimensional graphical representation of the state of stress at a point. The abscissa, , and ordinate …83

**telescope**— /tel euh skohp /, n., adj., v., telescoped, telescoping. n. 1. an optical instrument for making distant objects appear larger and therefore nearer. One of the two principal forms (refracting telescope) consists essentially of an objective lens… …84

**Pythagorean theorem**— See also: Pythagorean trigonometric identity The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) …85

**Douady rabbit**— in an exponential family …86

**Greek arithmetic, geometry and harmonics: Thales to Plato**— Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… …87

**Euclidean geometry**— geometry based upon the postulates of Euclid, esp. the postulate that only one line may be drawn through a given point parallel to a given line. [1860 65] * * * Study of points, lines, angles, surfaces, and solids based on Euclid s axioms. Its… …88

**Logic and the philosophy of mathematics in the nineteenth century**— John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… …89

**Euclidean geometry**— A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his… …90

**Polygon**— For other uses, see Polygon (disambiguation). Some polygons of different kinds In geometry a polygon (   …