By Saul Stahl

Tracing the formal improvement of Euclidean geometry, this article heavily follows Euclid's vintage, *Elements.* as well as delivering a old viewpoint on aircraft geometry, it covers comparable issues, together with non-neutral Euclidean geometry, circles and normal polygons, projective geometry, symmetries, inversions, knots and hyperlinks, and casual topology. comprises 1,000 perform difficulties. recommendations to be had. 2003 version.

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**Additional resources for Geometry from Euclid to Knots**

**Example text**

It is not necessarily in the center of the picture. glossary 26 center of a parallelogram – central vanishing point centrode – chord glossary centrode The instantaneous center of rotation of a rigid moving body. The centrode of two curves is the locus of the instantaneous center of rotation of a rigid body that has a point fixed on each curve. centroid The center of gravity of a geometric shape. For a triangle, it is the point of intersection of the three medians. cevian A segment from a vertex of a triangle to a point on the opposite side or its extension.

Brachistochrone problem The problem of determining the curve along which a bead sliding from rest and accelerated by gravity will travel from one point to another in the least time, assuming that there is no friction. The solution is part of a cycloid connecting the two points. braid A finite collection of disjoint vertical curves or strands in threedimensional space. The strands may weave over and under each other. Two braids are equivalent if one can be deformed into the other while keeping the endpoints of the strands fixed.

Cantor’s Axiom For every infinite sequence of segments such that each segment contains the next, there is a point contained in every segment in the sequence. Cantor set A fractal formed from a segment by removing the middle third without its endpoints, and then removing the middle thirds, without their endpoints, of the resulting two segments, and so on. The result is an infinite set of points. cap A region on a sphere whose boundary is a circle on the sphere. capacity See volume. capacity dimension See box-counting dimension.