Machu Picchu, Geometry Theorems and Problems, Online Education

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

Euclidean Geometry

Triangle, Angles

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

Cyclic Quadrilateral Index

Cyclic Quadrilateral.
Index 

Angle Bisector Index

Angle Bisector.
Index.

Abel Prize: Gromov, Drawing Parallels

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.

Angle Index

Angles.

Quadrilateral, Perpendicular, Squares, Area

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

Polygon Classification

Polygon Classification. Interactive Mind Map.

Sacred Geometry Index

Sacred Geometry.

Elearning 279: Tangent circles

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

Tangent Circles, Common External Tangent, Chord

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

Tangent Circles

Proposed Problem 277.
Tangent Circles, Common External Tangent.

Square, Circle, 90 Arc

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

Sagitta Problem

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

Sagitta, Arc, Chord

Sagitta, Arc, Chord.

Bisect an angle

Book I, Proposition 9: Bisect a given angle

Isoscele triangle 80-80-20

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

Isosceles Triangle Index

Isosceles Triangle.

Problem 273 Triangle and Squares

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

Cube of the external common tangent

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

Rhombus, Rhombuses, Rhombi

Rhombus.

Cube of the external common tangent

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

Heptagon index

Heptagons.

Classical Theorems

Classical Theorems.

Heptagon and Heptagram 

Heptagon and Heptagrams / Septegram.

Tangent circles, common tangent 

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

Circumcenter Index

Circumcenter. Index.

Pi: Irrational Math Constant

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.

Right triangle, Altitude, perpendiculars

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

Right triangle, Altitude, Catheti

Proposed Problem 268.
Right Triangle, Catheti and Altitude.

Right triangle, Catheti product

Proposed Problem 267.
Right Triangle, Product of Catheti.

Right triangle, Altitude, Geometric Mean

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

Albert Einstein at the age of 12

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

Pythagorean Theorem

Proposed Problem 265.
Right Triangle, Pythagorean Theorem.

Right triangle

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

Problem 263: Triangle, Median Projection

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

Regular hexagon inscribed in a circle

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

Heaxagons

Hexagons.

Regular pentagon inscribed

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

Pentagon Index

Pentagons.

Orthocenter Index

Orthocenter Index.

Centroid of a triangle Index

Centroid /Barycenter. Index.

Elearning 260: Problem about equilateral triangle

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

Elearning 259: Equilateral triangle, Incircle

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

Elearning 258: Equilateral triangle, Incircle

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

Problem 257: Equilateral triangle, circumcircle

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

Elearning 256: Equilateral triangle

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

Problem 254: Triangle and Centroid

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

Elearning 254: Triangle and Centroid

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

Elearning 253: Triangle, Centroid

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

Equilateral triangles

Equilateral Triangles Index.

Rectangle, Isosceles Right Triangle, Square, Area

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

Elearning 251: Parallelogram

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

Quadrilateral, diagonals, midpoints

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

Triangle sides, medians, squares

Proposed Problem 249.
Triangle sides, medians, squares.

Median Length theorem

Median length, Apollonius' Theorem

Euclid's Elements, Book II, Proposition 12

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

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

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

Elearning: Napoleon Theorem III

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

Napoleon Theorem II

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

Napoleon Theorem I

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

Elearning 245: Parallelogram

Proposed Problem 245. Parallelogram with Equilateral triangles

Elearning 244: Square center, diagonal

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

Elearning 243

Proposed Problem 243. Triangle with Equilateral triangles, Parallelogram.

Elearn 242: Equilateral triangle and parallelogram

Proposed Problem 242. Triangle with Equilateral triangles, Parallelogram.

Equilateral triangle, congruence SAS

Proposed Problem 241. Triangle with Equilateral triangles, Congruence.

Triangle with equilateral triangles

Proposed Problem 240. Triangle with Equilateral triangles, Parallelogram.

Square, Midpoint, Congruence, Pythagoras

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

Square. Midpoint, Congruence

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

Quadrilateral, midpoints

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

Quadrilateral, midpoints

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

Problem about Parallelogram and transversal

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

Problem 233: Parallelogram

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

Elearn 232: Parallelogram

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

Parallelograms Index

Parallelograms Index.

Elearn 232: Parallelogram, perpendicular lines

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

Geometry terms

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

Elearn 231: Triangle, Midpoint

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

Elearn 230: Triangle, Midpoint, Transversal

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

Elearn 229: Triangle, Centroid, Transversal

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

Elearn 228: Triangle, Midpoint

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

Elearn 227: Triangle, Centroid

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

Problem 226: Triangle, Centroid

Proposed Problem 226. Triangle, Centroid, Perpendicular lines.  

Viviani theorem extension, regular polygon

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

Viviani theorem, isosceles triangle, extension on the base

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

Viviani theorem, Isosceles triangle

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

Viviani theorem, Equilateral triangle, exterior point

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

Viviani's theorem I

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

Lune of Hippocrates Index

Lune of Hippocrates Index.  

Right triangle, inradius, altitude, arithmetic mean

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

Rhombus problem

Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean.

Elearn 218: Right triangle

Proposed Problem 218. Right triangle, Altitude and Projections.

Elearn 217: Right triangle, Altitude, Projections

Proposed Problem 217. Right triangle, Altitude and Projections.

Elearn: Quadrilateral, Angle Bisectors, Concurrency

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

Elearn 215: Cyclic quadrilateral

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

Elearn 214

Proposed Problem 214. Quadrilateral and Angle Bisectors.

Elearn 213 Triangle Inradius, Common Tangents

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

Elearn 212: 120 degree triangle, area

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

Archimedes Arbelos and Square

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

Archimedes Arbelos and Square

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

Elearn 211: 60 degree triangle, area

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

Elearn 210

Proposed Problem 210. Triangle, Angles, Auxiliary Lines.

Elearn 209

Proposed Problem 209. Triangle, Incircles, Inradius.

Clifford's theorem

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.
 

Elearn 208: Triangle, Angles

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

Problem 207: Hypotenuse

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

Elearn 206

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

Right triangle area

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

Elearn 204

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

Problem 203

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

Problem 202 Right triangle, excircles

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

Elearn 201

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

Elearning 200: Right Triangle

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

Problem: Triangle, Altitude, Angles

Proposed Problem 199. Triangle, Quadrilateral, Angles.

Geometry problem about angles and triangle

Proposed Problem 198. Triangle, Quadrilateral, Angles.

Elearning 197: Triangle Area

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

Elearning 196: Inradius, Exradii

Proposed Problem 196. Triangle, Inradius and Exradii Formula.

Triangle Centers Index.

Geometry: Triangle Area, inradius, exradii

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

Area of a triangle, semiperimeter, exradius

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

Area of a triangle, semiperimeter, inradius

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

Geometry Problem Circle, Diameter, and Chord

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

Geometry Problem 191 about triangle and squares

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

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