Problem 260: Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Square

Proposed Problem


See complete Problem 260 at:
gogeometry.com/problem/p260_equilateral_triangle_incircle_distance_square.htm

Level: High School, SAT Prep, College geometry

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Problem 259: Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares

Proposed Problem


See complete Problem 259 at:
gogeometry.com/problem/p259_equilateral_triangle_incircle_distance_square.htm

Level: High School, SAT Prep, College geometry

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Problem 258: Equilateral Triangle, Incircle, Point, Vertices, Side, Distances, Squares

Proposed Problem


See complete Problem 258 at:
gogeometry.com/problem/p258_equilateral_triangle_incircle_distance_square.htm

Level: High School, SAT Prep, College geometry

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Problem 257: Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares

Proposed Problem


See complete Problem 257 at:
gogeometry.com/problem/p257_equilateral_triangle_circumcircle_distance_sides.htm

Level: High School, SAT Prep, College geometry

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Problem 256: Equilateral Triangle, Circumcircle, Point, Vertices, Distances

Proposed Problem


See complete Problem 256 at:
gogeometry.com/problem/p256_equilateral_triangle_circumcircle_distance_vertex.htm

Level: High School, SAT Prep, College geometry

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Problem 255: Triangle, Centroid, Vertices, Interior/Exterior Point, Distances, Squares

Proposed Problem


See complete Problem 255 at:
gogeometry.com/problem/p255_triangle_centroid_squares_point_vertex.htm

Level: High School, SAT Prep, College geometry

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Problem 254: Triangle, Centroid, Vertices, Interior/Exterior Point, Distances, Squares

Proposed Problem


See complete Problem 254 at:
gogeometry.com/problem/p254_triangle_centroid_squares_interior_point.htm

Level: High School, SAT Prep, College geometry

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Pentagon Index

Theorems and Problems



See complete Pentagon Index at:
http://www.gogeometry.com/geometry/pentagon_polygon_shape_index_5_sides.html

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

Problem 253: Triangle, Centroid, Vertices, Distances, Squares

Proposed Problem


See complete Problem 253 at:
gogeometry.com/problem/p253_triangle_centroid_squares.htm

Level: High School, SAT Prep, College geometry

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Equilateral Triangle Index

Theorems and Problems



See complete Equilateral Triangle Index at:
gogeometry.com/geometry/equilateral_triangle_index_equal_sides.html

Level: High School, SAT Prep, College geometry

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Problem 19: Isosceles Right Triangle, Excenter, Perpendicular, Congruence

Proposed Problem
Try to use elementary geometry (Euclid's Elements)



See complete Problem 19 at:
gogeometry.com/problem/problem019.htm

Level: High School, SAT Prep, College geometry

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Problem 18: Right triangles, Angles, Congruence

Proposed Problem


See complete Problem 18 at:
gogeometry.com/problem/problem018.htm

Level: High School, SAT Prep, College geometry

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Problem 17: Right triangles and Angles

Proposed Problem


See complete Problem 17 at:
gogeometry.com/problem/problem017.htm

Level: High School, SAT Prep, College geometry

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Massacre of the Innocents by Peter Paul Rubens

Golden Rectangle
Peter Paul Rubens (1577 - 1640). Flemish painter, draughtsman and diplomat. He was the most versatile and influential Baroque artist of northern Europe in the 17th century. He is well-known for his Counter-Reformation altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects.

At a Sotheby's auction on July 10, 2002, Rubens' newly discovered painting Massacre of the Innocents sold for £49.5million ($76.2 million) to Lord Thomson. It is a current record for an Old Master painting.

Click the figure below to see the interactive illustration of Massacre of the Innocents by Peter Paul Rubens.



Continue reading at:
gogeometry.com/wonder_world/peter_paul_rubens_massacre_innocents_golden.html

New York City by Piet Mondrian

Golden Rectangle
Piet Mondrian was a Dutch painter, a pioneer of Geometric abstraction.

New York City (1941-42) Oil on canvas 119 x 114 cm (46 7/8 x 44 7/8 in) Musee national d'art moderne, Centre Georges Pompidou, Paris. In the further attempt to simplify and perfect his images, he did not use any curved lines or organic shapes, he used only straight lines and geometric shapes. He also only used black, white, gray, and the three primary colors – bright red, blue, and yellow. The use of his simple geometric shapes and basic colors formed a new style or art movement called De Stijl.

Click the figure below to see the interactive illustration of Piet Mondrian, New York City 1941-42.



Continue reading at:
gogeometry.com/wonder_world/piet_mondrian_broadway_boogie_woogie_golden.html

Piet Mondrian, Broadway Boogie Woogie

Golden Rectangle
Piet Mondrian was a Dutch painter, a pioneer of Geometric abstraction.

Broadway Boogie Woogie (1942-1943) Oil on canvas 50 x 50 in. (127 x 127 cm) The Museum of Modern Art, New York. It was his final painting, the checkerboard lines, are painted blue, gray, red and yellow. (The yellow was apparently inspired by New York’s Yellow cabs). In the further attempt to simplify and perfect his images, he did not use any curved lines or organic shapes, he used only straight lines and geometric shapes. He also only used black, white, gray, and the three primary colors – bright red, blue, and yellow. The use of his simple geometric shapes and basic colors formed a new style or art movement called De Stijl.

Click the figure below to see the interactive illustration of Piet Mondrian, Broadway Boogie Woogie.



Continue reading at:
gogeometry.com/wonder_world/piet_mondrian_broadway_boogie_woogie_golden.html

Paris Review, 1984 by Sol LeWitt and the Golden Rectangle

Golden Rectangle
Sol LeWitt (1928 - 2007) was an American artist linked to various movements, including Conceptual art and Minimalism. LeWitt , whose art is rooted in basic geometry, rose to fame in the late 1960s with his wall drawings and "structures" but was prolific in a wide range of media including drawing, printmaking, and painting.

Click the figure below to see the interactive illustration of Paris Review, 1984 by Sol LeWitt and Golden Rectangle.



Continue reading at:
gogeometry.com/wonder_world/sol_lewitt_paris_review_golden_rectangle.html

The Barolo Chapel or Cappella delle Brunate by Sol LeWitt

Golden Rectangle
Sol LeWitt (1928 - 2007) was an American artist linked to various movements, including Conceptual art and Minimalism. LeWitt , whose art is rooted in basic geometry, rose to fame in the late 1960s with his wall drawings and "structures" but was prolific in a wide range of media including drawing, printmaking, and painting.

Click the figure below to see the interactive illustration of The Barolo Chapel or Cappella delle Brunate by Sol LeWitt and Golden Rectangle.



Continue reading at:
gogeometry.com/wonder_world/sol_lewitt_brunate_golden_rectangle.html

Problem 16: Triangle, Cevian, Perpendicular, Angles, Congruence

Proposed Problem


See complete Problem 16 at:
http://gogeometry.com/problem/problem016.htm

Level: High School, SAT Prep, College geometry

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Problem 15: Triangle, Cevian, Angles, Congruence

Proposed Problem


See complete Problem 15 at:
http://gogeometry.com/problem/problem015.htm

Level: High School, SAT Prep, College geometry

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Problem 14: Triangle, Cevian, Midpoint, Angles

Proposed Problem


See complete Problem 14 at:
http://gogeometry.com/problem/problem014.htm

Level: High School, SAT Prep, College geometry

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Problem 13: Triangle, Angles, Congruence, Cevian

Proposed Problem


See complete Problem 13 at:
http://gogeometry.com/problem/problem013.htm

Level: High School, SAT Prep, College geometry

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Problem 12: Triangle, Cevian, Angles, Congruence

Proposed Problem


See complete Problem 12 at:
http://gogeometry.com/problem/problem012.htm

Level: High School, SAT Prep, College geometry

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Problem 11: Right triangle, Cevian, Angles

Proposed Problem


See complete Problem 11 at:
http://gogeometry.com/problem/problem011.htm

Level: High School, SAT Prep, College geometry

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Problem 252. Rectangle, isosceles right triangle, square, areas

Proposed Problem


See complete Problem 252 at:
gogeometry.com/problem/p252_rectangle_triangle_square_area.htm

Level: High School, SAT Prep, College geometry

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Theo van Doesburg: Arithmetic Composition. 1929-1930.

Golden Rectangle
Theo van Doesburg (1883 - 1931) was a Dutch artist, practicing in painting, writing, poetry and architecture. He is best known as the founder and leader of De Stijl.

De Stijl, also known as neoplasticism, was a Dutch artistic movement founded in 1917. Proponents of De Stijl sought to express a new utopian ideal of spiritual harmony and order. They advocated pure abstraction and universality by a reduction to the essentials of form and color; they simplified visual compositions to the vertical and horizontal directions, and used only primary colors along with black and white.

Click the figure below to see the interactive illustration of Arithmetic Composition.



Continue reading at:
gogeometry.com/wonder_world/theo_van_doesburg_arithmetic_composition_golden_rectangle.html

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

Proposed Problem


See complete Problem 251 at:
gogeometry.com/problem/p251_parallelogram_diagonal_square_area.htm

Level: High School, SAT Prep, College geometry

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Peru's 'The Milk of Sorrow' Takes Berlin Film Festival Top Award 2009

Golden Rectangle
'La Teta Asustada' a Peruvian drama about a young woman with a mysterious illness, won the Golden Bear award for the best movie at the Berlin Film Festival last night. Directed by Claudia Llosa, the film stars Magaly Solier as Fausta, who suffers from a disease she believes is transmitted through the breast milk of women who were raped in the Shining Path's war of terror in Peru. Her life starts to change direction after her mother dies and she goes to live in Lima.

Click the figure below to see the interactive illustration of Magaly Solier as Fausta.



Continue reading at:
gogeometry.com/wonder_world/berlin_festival_teta_asustada_milk_sorrow_golden_rectangle.html

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

Proposed Problem


See complete Problem 250 at:
gogeometry.com/problem/p250_quadrilateral_diagonals_midpoints_squares.htm

Level: High School, SAT Prep, College geometry

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Problem 249. Triangle sides, medians, squares

Proposed Problem


See complete Problem 249 at:
gogeometry.com/problem/p249_triangle_sides_medians_squares.htm

Level: High School, SAT Prep, College geometry

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Ilya Bolotowsky, Black Diamond, Screenprint, 1978

Golden Rectangle
Ilya Bolotowsky (Russian/American, 1907-1981) became a leading early 20th-century painter in abstract styles in New York City. His work, a search for philosophical order through visual expression, embraced Cubism and Geometric abstraction and was much influenced by Dutch painter Piet Mondrian.

Black Diamond, Screenprint, 1978. By 1950 Bolotowsky introduced circular and diamond-shaped canvases followed by ovals and other unusual rectangles.

Click the figure below to see the interactive illustration of Black Diamond, Screenprint, 1978.



Continue reading at:
gogeometry.com/wonder_world/ilya_bolotowsky_black_diamond_golden_rectangle.html

Homage to the Square, 1965 by Josef Albers

Golden Rectangle
Josef Albers (1888 - 1976) was a German-born American artist (geometric abstraction) and educator whose work, both in Europe and in the United States, formed the basis of some of the most influential and far-reaching art education programs of the 20th century.

Homage to the Square. These paintings investigated the retinal effects of color. He published the fruits of this systematic research in a volume called, the Interaction of Color in 1963. Albers used nested squares to investigate color interaction.

Click the figure below to see the interactive illustration of Homage to the Square, 1965.



Continue reading at:
gogeometry.com/wonder_world/josef_albers_homage_square_golden_rectangle.html

Piet Mondrian, Composition II in Red, Blue, and Yellow, 1930

Golden Rectangle
Piet Mondrian was a Dutch painter, a pioneer of Geometric abstraction.

In the further attempt to simplify and perfect his images, he did not use any curved lines or organic shapes, he used only straight lines and geometric shapes. He also only used black, white, gray, and the three primary colors – bright red, blue, and yellow. The use of his simple geometric shapes and basic colors formed a new style or art movement called De Stijl.

Click the figure below to see the interactive illustration of Composition II in Red, Blue, and Yellow.



Continue reading at:
gogeometry.com/wonder_world/piet_mondrian_composition_ii_golden_rectangle.html

Median length, Apollonius' Theorem

The following theorem has been attributed to Apollonius: In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side.



See complete illustration at:
gogeometry.com/geometry/median_length_apollonius_theorem.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

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

Acute Triangle


See complete illustration at:
gogeometry.com/geometry/euclid_elements_book_ii_proposition_13_cosines_law.htm

Level: High School, SAT Prep, College geometry

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

Obtuse Triangle


See complete illustration at:
gogeometry.com/geometry/euclid_elements_book_ii_proposition_12_cosines_law.htm

Level: High School, SAT Prep, College geometry

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Composition VII by Wassily Kandinsky

Kaleidoscope
One of the most famous 20th-century artists, he is credited with painting the first modern abstract works. Kandinsky analyses in his writings the geometrical elements which compose every painting, namely the point and the line, as well as the physical support and the material surface on which the artist draws or paints and which he calls the basic plan.
Click the figure below to see the interactive illustration.


Continue reading at:
gogeometry.com/wonder_world/wassily_kandinsky_composition_vii_1.html

"On White II" by Wassily Kandinsky

Kaleidoscope
One of the most famous 20th-century artists, he is credited with painting the first modern abstract works. Kandinsky analyses in his writings the geometrical elements which compose every painting, namely the point and the line, as well as the physical support and the material surface on which the artist draws or paints and which he calls the basic plan.
Click the figure below to see the interactive illustration.


Continue reading at:
http://gogeometry.com/wonder_world/wassily_kandinsky_on_white_ii_1.html

Composition X by Wassily Kandinsky

Kaleidoscope
One of the most famous 20th-century artists, he is credited with painting the first modern abstract works. Kandinsky analyses in his writings the geometrical elements which compose every painting, namely the point and the line, as well as the physical support and the material surface on which the artist draws or paints and which he calls the basic plan.
Click the figure below to see the interactive illustration.


Continue reading at:
gogeometry.com/wonder_world/wassily_kandinsky_composition_x_1.html

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

Inner Napoleon Triangle


See complete Problem 248 at:
gogeometry.com/problem/p248_napoleon_theorem_iii_area_inner_outer.htm

Level: High School, SAT Prep, College geometry

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Problem 247. Napoleon's Theorem II. Internal Equilateral triangles

Inner Napoleon Triangle


See complete Problem 247 at:
gogeometry.com/problem/p247_napoleon_theorem_inner_equilateral_triangle.htm

Level: High School, SAT Prep, College geometry

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Ekaterina Gordeeva and the Golden Rectangle

Golden Rectangle
Ekaterina Gordeeva (born May 28, 1971) often called Katia, Gordeeva is a Russian (former Soviet) pair skater. Together with her late partner and husband Sergei Grinkov, she was the 1988 and 1994 Olympic Champion.

Click the figure below to see the interactive illustration.



Continue reading at:
gogeometry.com/wonder_world/ekaterina_gordeeva_golden_rectangle.html

Lake Erie and the Golden Rectangle

Lake Erie is the fourth largest lake (by surface area) of the five Great Lakes, and the tenth largest globally.

On February 7, 2009, New York Times reported that one man died after more than 100 ice fisherman who ventured a mile onto the western Ohio shores of Lake Erie Saturday had to be rescued after an eight-mile long portion of ice they were on broke away amid warming conditions and starting drifting north.

An ice floe is a floating chunk of ice that is less than 10 kilometers (six miles) in its greatest dimension. Wider chunks of ice are called ice fields.

Click the figure below to see the interactive illustration of Lake Erie and the Golden Rectangle.



Continue reading at:
gogeometry.com/wonder_world/lake_erie_golden_rectangle.html

Alex Rodriguez and the Golden Rectangle

Golden Rectangle
Alex Rodriguez is a Dominican American Major League Baseball player. He currently plays third baseman for the New York Yankees. Rodriguez has been cited as among the best all–around players currently in Major League Baseball. He has also been compared with many all-time great players.

In February 2009, Sports Illustrated reported that Alex Rodriguez tested positive for anabolic steroids in 2003, the year in which baseball players were tested anonymously and without penalty to assess the level of steroid use in the game.

Click the figure below to see the interactive illustration.



Continue reading at:
gogeometry.com/wonder_world/alex_rodriguez_baseball_golden_rectangle.html

Versatile actor James Whitmore died of lung cancer

Golden Rectangle
James Whitmore (October 1, 1921 – February 6, 2009) was an American two-time Oscar Academy Award-nominated, Emmy- and Golden Globe-winning film actor. Whitmore died of lung cancer, Friday, Feb. 6, 2009, in his Malibu home, according to his son Steve Whitmore.
Click the figure below to see the interactive illustration.



Continue reading at:
gogeometry.com/wonder_world/whitmore_james_dead_golden_rectangle.html

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

Outer Napoleon Triangle


See complete Problem 246 at:
gogeometry.com/problem/p246_napoleon_theorem_external_equilateral_triangle.htm

Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 245: Parallelogram with Equilateral triangles. Congruence

See complete Problem 245 at:
gogeometry.com/problem/p245_parallelogram_equilateral_triangle_congruence.htm

Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 244: Squares, Diagonals, Centers, Distance

See complete Problem 244 at:
gogeometry.com/problem/p244_square_centers_diagonal_vertex.htm

Level: High School, SAT Prep, College geometry

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Triangle with Equilateral triangles, Rhombuses, Parallelograms

See complete Problem 243 at:
gogeometry.com/problem/p243_triangle_equilateral_parallelograms.htm

Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 242: Triangle with Equilateral triangles, Parallelogram

See complete Problem 242 at:
gogeometry.com/problem/p242_triangle_equilateral_parallelogram.htm

Level: High School, SAT Prep, College geometry

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