Geometry Theorems and Problems - Recent Additions (Page 10 of 15)

Proposed Problem 281.
Triangles, Angles, Isosceles, Equilateral.

Cyclic Quadrilateral.
Index 

Angle Bisector.
Index.

Drawing parallels in geometry.
Mikhail Gromov has been awarded the Abel Prize for his work making sense of the range of geometries that appeared in the 19th century and he is a worthy successor to the likes of Euclid, Riemann and Gauss, Bolyai and Lobachevsky.

Angles.

Proposed Problem 280.
Quadrilateral, Perpendiculars, Area of Squares.

Polygon Classification. Interactive Mind Map.

Sacred Geometry.

Proposed Problem 279.
Tangent Circles, Common External Tangent, Chords, Inradius.

Proposed Problem 278.
Tangent Circles, Common External Tangent, Chord.

Proposed Problem 277.
Tangent Circles, Common External Tangent.

Proposed Problem 276.
Square, 90 degree Arcs, Circle, Radius.

Proposed Problem 275.
Right Triangle, Circumcircle, Sagitta, Inradius.

Sagitta, Arc, Chord.

Book I, Proposition 9: Bisect a given angle

Proposed Problem 274.
Isosceles Triangle, 80-80-20, Angles.

Isosceles Triangle.

Proposed Problem 273.
Triangle, Perpendiculars, Area of Squares.

Proposed Problem 272.
Tangent Circles, the Cube of the Common external tangent.

Rhombus.

Proposed Problem 271.
Tangent Circles, the Cube of the Common external tangent.

Heptagons.

Classical Theorems.

Heptagon and Heptagrams / Septegram.

Proposed Problem 270.
Tangent Circles, Common external tangent, Fractional exponents.

Circumcenter. Index.

Pi Day.
Saturday, March 14, 2009 = 3.14
It's time to get irrational. Tomorrow is Pi Day, when mathematicians will gather to celebrate the mystery of science's most famous strange number.

Proposed Problem 269.
Right Triangle, Altitude, Perpendicular, Projection.

Proposed Problem 268.
Right Triangle, Catheti and Altitude.

Proposed Problem 267.
Right Triangle, Product of Catheti.

Proposed Problem 266.
Right Triangle, Altitude, Geometric Mean.

Albert Einstein and the Pythagorean theorem.
A preteen Albert Einstein devised a new proof of the Pythagorean theorem.

Proposed Problem 265.
Right Triangle, Pythagorean Theorem.

Proposed Problem 264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean.

Proposed Problem 263.
Triangle, Median, Altitude, Orthogonal Projection, Sides.

Proposed Problem 262.
Regular Hexagon inscribed in a circle, sum of distances.

Hexagons.

Proposed Problem 261.
Regular Pentagon inscribed in a circle, sum of distances.

Pentagons.

Orthocenter Index.

Centroid /Barycenter. Index.

Proposed Problem 260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.

Proposed Problem 259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.

Proposed Problem 258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Proposed Problem 257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Proposed Problem 256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.

Proposed Problem 255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.

Proposed Problem 254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.

Proposed Problem 253.
Triangle, Centroid, Vertices, Distances, Squares.

Equilateral Triangles Index.

Proposed Problem 252.
Rectangle, isosceles right triangle, square, area.

Proposed Problem 251.
Parallelogram, sides, diagonals, squares, areas.

Proposed Problem 250.
Quadrilateral, sides, diagonals, midpoints, squares.

Proposed Problem 249.
Triangle sides, medians, squares.

Median length, Apollonius' Theorem

Euclid's Elements Book II, Proposition 12: Law of Cosines.

Euclid's Elements Book II, Proposition 13: Law of Cosines.

Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

Proposed Problem 247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon triangle.

Proposed Problem 246.
Napoleon's Theorem I. External Equilateral triangles.

Proposed Problem 245. Parallelogram with Equilateral triangles

Proposed Problem 244. Square, Diagonals, Centers, Distance.

Proposed Problem 243. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 242. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 241. Triangle with Equilateral triangles, Congruence.

Proposed Problem 240. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 239. Square, Midpoints, Lines, Congruence, Pythagoras.

Proposed Problem 238. Square, Midpoints, Lines, Congruence.

Proposed Problem 237. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.

Proposed Problem 236. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.

Proposed Problem 235. Parallelogram, Transversal line, Perpendicular lines.  

Proposed Problem 234. Parallelogram, Line through a vertex, Perpendicular lines.

Proposed Problem 233. Parallelogram, Exterior line, Perpendicular lines.

Parallelograms Index.

Proposed Problem 232. Parallelogram, Line through a vertex, Perpendicular lines.

Geometry Online Glossary .
Geometry Glossary based on the new New York State mathematics standards initiative.

Proposed Problem 231. Triangle, Midpoints, Transversal, Perpendicular lines.

Proposed Problem 230. Triangle, Midpoints, Transversal, Perpendicular lines.

Proposed Problem 229. Triangle, Centroid, Transversal, Perpendicular lines.

Proposed Problem 228. Triangle, Midpoints, Exterior line, Perpendiculars lines.

Proposed Problem 227. Triangle, Centroid, Exterior line, Perpendicular lines.  

Proposed Problem 226. Triangle, Centroid, Perpendicular lines.  

Proposed Problem 225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance.  

Proposed Problem 224. Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base.  

Proposed Problem 223. Viviani's theorem, Isosceles triangle, Altitude, Distances.  

Proposed Problem 222. Viviani's theorem, Equilateral triangle, Exterior point, Distances.  

Proposed Problem 221. Viviani's theorem, Equilateral triangle, Interior point, Distances.  

Lune of Hippocrates Index.  

Proposed Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.  

Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean.

Proposed Problem 218. Right triangle, Altitude and Projections.

Proposed Problem 217. Right triangle, Altitude and Projections.

Proposed Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.

Proposed Problem 215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral.

Proposed Problem 214. Quadrilateral and Angle Bisectors.

Proposed Problem 213. Triangle, Incircle, Inradius, Semicircles, Common Tangents.

Proposed Problem 212. 120 Degree Triangle, Equilateral triangles, Areas.

Archimedes Arbelos and Square 2. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation.

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation.

Proposed Problem 211. 60 Degree Triangle, Equilateral triangles, Areas.

Proposed Problem 210. Triangle, Angles, Auxiliary Lines.

Proposed Problem 209. Triangle, Incircles, Inradius.

Clifford's Circle Chain Theorems. This is a step by step presentation of the first theorem. Clifford discovered, in the ordinary Euclidean plane, a "sequence or chain of theorems" of increasing complexity, each building on the last in a natural progression.
 

Proposed Problem 208. Triangle, Excircles, Angles, 360 degrees.  

Proposed Problem 207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse.  

Problem 206. Area of a Right Triangle, Inradius, and Exradius relative to the hypotenuse.  

Proposed Problem 205. Right Triangle Area, Exradii relatives to legs or catheti.  

Proposed Problem 204. Right Triangle, Incircle, Excircles, Inradius, Exradii.  

Proposed Problem 203. Right Triangle, Excircles, Exradii, Hypotenuse.

Proposed Problem 202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter.  

Proposed Problem 201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter.  

Proposed Problem 200. Right Triangle, Incircle, Excircles, Points of Tangency, Inradius.

Proposed Problem 199. Triangle, Quadrilateral, Angles.

Proposed Problem 198. Triangle, Quadrilateral, Angles.

Proposed Problem 197. Area of a Triangle, Side, Inradius, and Exradius.

Proposed Problem 196. Triangle, Inradius and Exradii Formula.

Triangle Centers Index.

Proposed Problem 195. Area of a Triangle, Inradius, Exradii.  

Proposed Problem 194. Area of a Triangle, Semiperimeter, Exradius.

Proposed Problem 193. Area of a Triangle, Semiperimeter, Inradius.

Proposed Problem 192. Circle, Diameter, Chord, Perpendicular, Triangle, Area.

Proposed Problem 191. Triangle, Altitudes, Orthocenter, Squares, Areas.