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Magic circle (mathematics) – Chinese mathematical arrangement; Malfatti circles – Three tangent circles in a triangle; Nine-point circle – Circle constructed from a triangle; Orthocentroidal circle – Circle constructed from a triangle; Osculating circle – Circle of immediate corresponding curvature of a curve at a point
Placement exams or placement tests assess abilities in English, mathematics and reading; they may also be used in other disciplines such as foreign languages, computer and internet technologies, health and natural sciences. The goal is to offer low-scoring students remedial coursework (or other remediation) to prepare them for regular coursework.
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
A math circle is an extracurricular activity intended to enrich students' understanding of mathematics. The concept of math circle came into being in the erstwhile USSR and Bulgaria, around 1907, with the very successful mission to "discover future mathematicians and scientists and to train them from the earliest possible age". [1]
In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
As a high school student, Stevens was a student of the Ross Program, an experience which would later lead him to found the PROMYS [1] program along with fellow Ross alumni Marjory Baruch, David Fried, and Steve Rosenberg.
Another argument for the impossibility of circular realizations, by Helge Tverberg, uses inversive geometry to transform any three circles so that one of them becomes a line, making it easier to argue that the other two circles do not link with it to form the Borromean rings. [27] However, the Borromean rings can be realized using ellipses. [2]