Geometry: An Interactive Journey to Mastery

IUDFWDOGLPHQVLRQͼ௘௘ͽ: If a fractal is composed of N parts, each a scaled copy of the original fractal with scale

factor kWKHQLWVIUDFWDOGLPHQVLRQLVWKHQXPEHUd so that kd (^) N^1. 6HHDOVRfractal.
JHRPHWU\ͼ௘௘ͽ7KHEUDQFKRIPDWKHPDWLFVFRQFHUQHGZLWKWKHSURSHUWLHVRIVSDFHDQGRI¿JXUHVOLQHV
curves, points, and shapes drawn in space. 6HHDOVRplanar geometry, three-dimensional geometry,
spherical geometry.
JOLGHUHÀHFWLRQͼ௘௘ͽ$JOLGHUHÀHFWLRQDORQJDOLQHL in a plane is the mapping that results from performing a
translation in a direction parallel to LIROORZHGE\DUHÀHFWLRQDERXWL.6HHDOVRmapping.
K\SHUERODͼ௘௘ͽ: Given two points F and G in the plane, the set of all points P for which the differences of
distances FPíPG and GPíPFKDYHWKHVDPHFRQVWDQWYDOXHWUDFHVDFXUYHFDOOHGDK\SHUEROD7KHSRLQWVF
and GDUHFDOOHGWKHIRFLRIWKHK\SHUEROD
K\SRWHQXVHͼ௘௘ͽ: The side opposite the right angle in a right triangle.
LQFHQWHURIDWULDQJOHͼ௘௘ͽ: The center of the incircle of a triangle is its incenter. It is the location where the
WKUHHDQJOHELVHFWRUVRIWKHWULDQJOHFRLQFLGH6HHDOVRincircle of a triangle.
LQFLUFOHRIDWULDQJOHͼ௘௘ͽ: For each triangle, there is a unique circle sitting inside the triangle tangent to each
of its three sides. This circle is the incircle of the triangle.
LQGXFWLYHUHDVRQLQJͼ௘௘ͽ: 7KHSURFHVVRI¿QGLQJSDWWHUQVDQGPDNLQJFRQMHFWXUHVEDVHGRQWKRVHSDWWHUQV
LQVFULEHGDQJOHͼ௘௘ͽ: If P and Q are two endpoints of an arc of a circle and A is a point on the circle not on the
arc, then ‘PAQLVDQLQVFULEHGDQJOH
LVRPHWU\ͼ௘௘ͽ$PDSSLQJWKDWSUHVHUYHVGLVWDQFHVEHWZHHQSRLQWV6HHDOVRmapping.
LVRSHULPHWULFSUREOHPͼ௘௘ͽ7KHFKDOOHQJHRIGHWHUPLQLQJZKLFK¿JXUHLQWKHSODQHKDVWKHJUHDWHVWDUHDJLYHQ
D¿[HGOHQJWKIRULWVSHULPHWHU
LVRVFHOHVWULDQJOHͼ௘௘ͽ: $WULDQJOHZLWKDWOHDVWWZRVLGHVFRQJUXHQWLVLVRVFHOHV
ODWHUDOͼ௘௘ͽ: 5HIHUVWRDQ\IHDWXUHRIDFRQHRUF\OLQGHUWKDWLVQRWSDUWRIDEDVHRIWKH¿JXUHͼ௘)RUH[DPSOHD
ODWHUDOHGJHLVDQ\HGJHRIWKH¿JXUHWKDWLVQRWDQHGJHRIDEDVHRUDODWHUDOIDFHLVDQ\IDFHRIWKH¿JXUHWKDWLV
QRWDEDVH௘ͽ6HHDOVR cone, cylinder.
PDSSLQJͼ௘௘ͽ$PDSSLQJRIWKHSODQHLVDUXOHWKDWVKLIWVVRPHRUDOOSRLQWVRIWKHSODQHWRQHZORFDWLRQV
in the plane.