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, 808020, 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.
StepbyStep construction, Manipulation, and animation. 

Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
StepbyStep 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.
