Black and white outline flag of Nepal. Red with a blue border around the unique shape of two overlapping right triangles; the smaller, upper triangle bears a white stylized moon and the larger, lower triangle bears a white 12-pointed sun

Flag of Nepal, 2009

Black and white outline flag of Nepal. Red with a blue border around the unique shape of two overlapping…

Color flag of Papua New Guinea. Divided diagonally from upper hoist-side corner; the upper triangle is red with a soaring yellow bird of paradise centered; the lower triangle is black with five, white, five-pointed stars of the Southern Cross constellation centered.

Flag of Papua New Guinea, 2009

Color flag of Papua New Guinea. Divided diagonally from upper hoist-side corner; the upper triangle…

Color flag of Philippines. Two equal horizontal bands of blue (top; representing peace and justice) and red (representing courage); a white equilateral triangle based on the hoist side represents equality; the center of the triangle displays a yellow sun with eight primary rays, each representing one of the first eight provinces that sought independence from Spain; each corner of the triangle contains a small, yellow, five-pointed star representing the three major geographical divisions of the country: Luzon, Visayas, and Mindanao; the design of the flag dates to 1897; in wartime the flag is flown upside down with the red band at the top.

Flag of Philippines, 2009

Color flag of Philippines. Two equal horizontal bands of blue (top; representing peace and justice)…

Black and white outline flag of Philippines. Two equal horizontal bands of blue (top; representing peace and justice) and red (representing courage); a white equilateral triangle based on the hoist side represents equality; the center of the triangle displays a yellow sun with eight primary rays, each representing one of the first eight provinces that sought independence from Spain; each corner of the triangle contains a small, yellow, five-pointed star representing the three major geographical divisions of the country: Luzon, Visayas, and Mindanao; the design of the flag dates to 1897; in wartime the flag is flown upside down with the red band at the top

Flag of Philippines, 2009

Black and white outline flag of Philippines. Two equal horizontal bands of blue (top; representing peace…

Black and white flag of Puerto Rico. Five equal horizontal bands of red (top and bottom) alternating with white; a blue isosceles triangle based on the hoist side bears a large, white, five-pointed star in the center; design initially influenced by the US flag, but similar to the Cuban flag, with the colors of the bands and triangle reversed.

Flag of Puerto Rico, 2009

Black and white flag of Puerto Rico. Five equal horizontal bands of red (top and bottom) alternating…

Black and white outline flag of Puerto Rico. Five equal horizontal bands of red (top and bottom) alternating with white; a blue isosceles triangle based on the hoist side bears a large, white, five-pointed star in the center; design initially influenced by the US flag, but similar to the Cuban flag, with the colors of the bands and triangle reversed

Flag of Puerto Rico, 2009

Black and white outline flag of Puerto Rico. Five equal horizontal bands of red (top and bottom) alternating…

Color flag of Saint Kitts and Nevis. Divided diagonally from the lower hoist side by a broad black band bearing two white, five-pointed stars; the black band is edged in yellow; the upper triangle is green, the lower triangle is red.

Flag of Saint Kitts and Nevis, 2009

Color flag of Saint Kitts and Nevis. Divided diagonally from the lower hoist side by a broad black band…

Black and white outline flag of Saint Kitts and Nevis. Divided diagonally from the lower hoist side by a broad black band bearing two white, five-pointed stars; the black band is edged in yellow; the upper triangle is green, the lower triangle is red

Flag of Saint Kitts and Nevis, 2009

Black and white outline flag of Saint Kitts and Nevis. Divided diagonally from the lower hoist side…

Color flag of Saint Lucia. Blue, with a gold isosceles triangle below a black arrowhead; the upper edges of the arrowhead have a white border.

Flag of Saint Lucia, 2009

Color flag of Saint Lucia. Blue, with a gold isosceles triangle below a black arrowhead; the upper edges…

Black and white outline flag of Saint Lucia. Blue, with a gold isosceles triangle below a black arrowhead; the upper edges of the arrowhead have a white border

Flag of Saint Lucia, 2009

Black and white outline flag of Saint Lucia. Blue, with a gold isosceles triangle below a black arrowhead;…

Color flag of Sao Tome and Principe. Three horizontal bands of green (top), yellow (double width), and green with two black five-pointed stars placed side by side in the center of the yellow band and a red isosceles triangle based on the hoist side; uses the popular pan-African colors of Ethiopia.

Flag of Sao Tome and Principe, 2009

Color flag of Sao Tome and Principe. Three horizontal bands of green (top), yellow (double width), and…

Black and white outline flag of Sao Tome and Principe. Three horizontal bands of green (top), yellow (double width), and green with two black five-pointed stars placed side by side in the center of the yellow band and a red isosceles triangle based on the hoist side; uses the popular pan-African colors of Ethiopia

Flag of Sao Tome and Principe, 2009

Black and white outline flag of Sao Tome and Principe. Three horizontal bands of green (top), yellow…

Color flag of Slovenia. Three equal horizontal bands of white (top), blue, and red, with the Slovenian seal (a shield with the image of Triglav, Slovenia's highest peak, in white against a blue background at the center; beneath it are two wavy blue lines depicting seas and rivers, and above it are three six-pointed stars arranged in an inverted triangle, which are taken from the coat of arms of the Counts of Celje, the great Slovene dynastic house of the late 14th and early 15th centuries); the seal is in the upper hoist side of the flag centered on the white and blue bands.

Flag of Slovenia, 2009

Color flag of Slovenia. Three equal horizontal bands of white (top), blue, and red, with the Slovenian…

Black and white outline flag of Slovenia. Three equal horizontal bands of white (top), blue, and red, with the Slovenian seal (a shield with the image of Triglav, Slovenia's highest peak, in white against a blue background at the center; beneath it are two wavy blue lines depicting seas and rivers, and above it are three six-pointed stars arranged in an inverted triangle, which are taken from the coat of arms of the Counts of Celje, the great Slovene dynastic house of the late 14th and early 15th centuries); the seal is in the upper hoist side of the flag centered on the white and blue bands

Flag of Slovenia, 2009

Black and white outline flag of Slovenia. Three equal horizontal bands of white (top), blue, and red,…

Color flag of Solomon Islands. Divided diagonally by a thin yellow stripe from the lower hoist-side corner; the upper triangle (hoist side) is blue with five white five-pointed stars arranged in an X pattern; the lower triangle is green.

Flag of Solomon Islands, 2009

Color flag of Solomon Islands. Divided diagonally by a thin yellow stripe from the lower hoist-side…

Black and white outline flag of Solomon Islands. Divided diagonally by a thin yellow stripe from the lower hoist-side corner; the upper triangle (hoist side) is blue with five white five-pointed stars arranged in an X pattern; the lower triangle is green

Flag of Solomon Islands, 2009

Black and white outline flag of Solomon Islands. Divided diagonally by a thin yellow stripe from the…

Color flag of South Africa. Two equal width horizontal bands of red (top) and blue separated by a central green band that splits into a horizontal Y, the arms of which end at the corners of the hoist side; the Y embraces a black isosceles triangle from which the arms are separated by narrow yellow bands; the red and blue bands are separated from the green band and its arms by narrow white stripes.

Flag of South Africa, 2009

Color flag of South Africa. Two equal width horizontal bands of red (top) and blue separated by a central…

Black and white outline flag of South Africa. Two equal width horizontal bands of red (top) and blue separated by a central green band that splits into a horizontal Y, the arms of which end at the corners of the hoist side; the Y embraces a black isosceles triangle from which the arms are separated by narrow yellow bands; the red and blue bands are separated from the green band and its arms by narrow white stripes

Flag of South Africa, 2009

Black and white outline flag of South Africa. Two equal width horizontal bands of red (top) and blue…

Color flag of Sudan. Three equal horizontal bands of red (top), white, and black with a green isosceles triangle based on the hoist side.

Flag of Sudan, 2009

Color flag of Sudan. Three equal horizontal bands of red (top), white, and black with a green isosceles…

Black and white outline flag of Sudan. Three equal horizontal bands of red (top), white, and black with a green isosceles triangle based on the hoist side

Flag of Sudan, 2009

Black and white outline flag of Sudan. Three equal horizontal bands of red (top), white, and black with…

Color flag of Thailand. Divided diagonally by a yellow-edged black band from the lower hoist-side corner; the upper triangle (hoist side) is green and the lower triangle is blue.

Flag of Thailand, 2009

Color flag of Thailand. Divided diagonally by a yellow-edged black band from the lower hoist-side corner;…

Black and white outline flag of Thailand. Divided diagonally by a yellow-edged black band from the lower hoist-side corner; the upper triangle (hoist side) is green and the lower triangle is blue

Flag of Thailand, 2009

Black and white outline flag of Thailand. Divided diagonally by a yellow-edged black band from the lower…

Color flag of Togo. Red, with a black isosceles triangle (based on the hoist side) superimposed on a slightly longer yellow arrowhead that extends to the center of the flag; a white star is in the center of the black triangle.

Flag of Togo, 2009

Color flag of Togo. Red, with a black isosceles triangle (based on the hoist side) superimposed on a…

Black and white outline flag of Togo. Red, with a black isosceles triangle (based on the hoist side) superimposed on a slightly longer yellow arrowhead that extends to the center of the flag; a white star is in the center of the black triangle

Flag of Togo, 2009

Black and white outline flag of Togo. Red, with a black isosceles triangle (based on the hoist side)…

Color flag of Zimbabwe. Seven equal horizontal bands of green, yellow, red, black, red, yellow, and green with a white isosceles triangle edged in black with its base on the hoist side; a yellow Zimbabwe bird representing the long history of the country is superimposed on a red five-pointed star in the center of the triangle, which symbolizes peace; green symbolizes agriculture, yellow - mineral wealth, red - blood shed to achieve independence, and black stands for the native people.

Flag of Zimbabwe, 2009

Color flag of Zimbabwe. Seven equal horizontal bands of green, yellow, red, black, red, yellow, and…

Black and white outline flag of Zimbabwe. Seven equal horizontal bands of green, yellow, red, black, red, yellow, and green with a white isosceles triangle edged in black with its base on the hoist side; a yellow Zimbabwe bird representing the long history of the country is superimposed on a red five-pointed star in the center of the triangle, which symbolizes peace; green symbolizes agriculture, yellow - mineral wealth, red - blood shed to achieve independence, and black stands for the native people

Flag of Zimbabwe, 2009

Black and white outline flag of Zimbabwe. Seven equal horizontal bands of green, yellow, red, black,…

Illustration used to inscribe a circle in a given triangle.

Construction Used to Inscribe a Circle in a Triangle

Illustration used to inscribe a circle in a given triangle.

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of a triangle and to the the other two sides prolonged is said to be escribed to the triangle."

Construction Used to Escribe a Circle to a Triangle

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of…

Illustration used to circumscribe a circle about a given triangle.

Construction Used to Circumscribe a Circle About a Triangle

Illustration used to circumscribe a circle about a given triangle.

Illustration of three isosceles triangles with the same base AC but varying heights (as B gets farther from the base).

3 Isosceles Triangles Wit Equal Bases

Illustration of three isosceles triangles with the same base AC but varying heights (as B gets farther…

Illustration of a circle used to prove "Any angle inscribed in a segment less than a semicircle is an obtuse angle."

Obtuse Angles Inscribed in Circle Proof

Illustration of a circle used to prove "Any angle inscribed in a segment less than a semicircle is an…

"Aberia Caffra, Hook. f. & Harv. Fig. 59. Thorny, glabrous: lvs. obovate, obtuse, cuneate at base, entire:fls. diaecious, apetalous. G. c. III. 18:737. R. H. 1904:256. -The kei apple of the Cape of Good Hope; a spiny plant grown S. for hedges; is considered promising for S. Calif. and S. Fla. as a fr. plant. Fruit acid, used as pickles or conserves. Proves quite hardy in S. Calif." L.H. Bailey, 1917

Aberia Caffra

"Aberia Caffra, Hook. f. & Harv. Fig. 59. Thorny, glabrous: lvs. obovate, obtuse, cuneate at base, entire:fls.…

"Latifolia, perennial: whole plant viscid-pubescent, prostrate: lvs. thick, ovate, orbicular or reniform, obtuse, stalked: fls. fragrant, 1/2 - 3/4 in. long, lemon yellow. June, July" L.H. Bailey, 1917

Coastal Sand Verbena

"Latifolia, perennial: whole plant viscid-pubescent, prostrate: lvs. thick, ovate, orbicular or reniform,…

An illustration of a ornate triangle shaped doodad.

Triangle Shaped Doodad

An illustration of a ornate triangle shaped doodad.

'Rhynchops. Skimmer. Bill hypognathous Among the singular bills of birds that frequently excite our wonder, that of the skimmers as one of the most anomalous. The under mandible is much longer than the upper, compressed like a knife-blade; its end is obtuse; its sides come abruptly together and are completely soldered; the upper edge is as sharp as the under, and fits a groove in the upper mandible; the jawbone, viewed apart, looks like a short-handled pitchfork. The upper mandible in also compressed, but less so, nor is it so obtuse at the end; its substance is nearly hallow, with light cancellated structure, much as in a toucan; it is freely movable by means of an elastic hinge at the forehead." Elliot Coues, 1884

The Bill of a Skimmer

'Rhynchops. Skimmer. Bill hypognathous Among the singular bills of birds that frequently excite our…

The Tomb of Atreus also known as the Treasury of Atreus is a tomb located in Mycenae, Greece built between 1250 and 1300 B.C. The face of the tomb consists of columns and has a triangle above the doorway. The tomb has an interior that is formed of a semi-underground circular room with a beehive tomb, also known as the tholos.

Tomb of Atreus

The Tomb of Atreus also known as the Treasury of Atreus is a tomb located in Mycenae, Greece built between…

"Simorhynchus pusillus. Least Auk. Knob-nosed Auk. Bill small and simple, but stout for its length, scarcely higher than wide at base, rather obtuse at tip. A small knob or tubercle at the base of the culmen, which is deciduous. No crest; but front, and sides of head more or less thickly lined with delicate white thready feathers; a similar series, exceedingly fine, from the eye along sides of hind head and nape. Excepting these filaments, the entire upper parts glossy black; region about under mandible, and a few feathers along the sides of body and flanks, blackish; under parts white, more or less extensively mottles or clouded with blackish. Lining of wings white, with dark feathers along edge. Bill red, the know and base of upper mandible dark. Legs (dry) undefinably dark, the front of tarsus and tops of toes lighter." Elliot Coues, 1884

Least Auks

"Simorhynchus pusillus. Least Auk. Knob-nosed Auk. Bill small and simple, but stout for its length,…

"Simorhynchus pusillus. Least Auk. Knob-nosed Auk. Bill small and simple. but stout for its length, scarcely higher than wide at base, rather obtuse at tip. A small knob or tubercle at the base of the culmen, which is deciduous." Elliot Coues, 1884

Least Auk Adult

"Simorhynchus pusillus. Least Auk. Knob-nosed Auk. Bill small and simple. but stout for its length,…

"Simorhynchus pusillus. Least Auk. Knob-nosed Auk. Bill small and simple. but stout for its length, scarcely higher than wide at base, rather obtuse at tip." Elliot Coues, 1884

Least Auk Adult

"Simorhynchus pusillus. Least Auk. Knob-nosed Auk. Bill small and simple. but stout for its length,…

"Alle. Sea Dove. Size small. Bill very short, stout, and obtuse, as well as high at base, the sides of both mandibles turgid, the edge of the upper much infected; culmen very convex; rictus ample, decurved at end; gonys straight, very short, the mandibular rami correspondingly long, and widely divaricated; nasal fossae short, wide, deep, partly, patly feathered. Nostrils sub basal, more nearly circular than in any other genus excepting the next." Elliot Coues, 1884

Sea Dove Bill

"Alle. Sea Dove. Size small. Bill very short, stout, and obtuse, as well as high at base, the sides…

"Uria columba. Pigeon Guillemot. Bill stouter than that of grylle, and more obtuse." Elliot Coues, 1884

Pigeon Guillemot Bill

"Uria columba. Pigeon Guillemot. Bill stouter than that of grylle, and more obtuse." Elliot Coues, 1884

Silhouette outlines of shapes (quadrilateral, hexagon, arrow, pentagon) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Shapes Silhouette Tangram Card #2

Silhouette outlines of shapes (quadrilateral, hexagon, arrow, pentagon) made from tangram pieces. Tangrams,…

Solutions for silhouette outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Silhouette Solution Tangram Card

Solutions for silhouette outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces.…

Solutions for silhouette outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Silhouette Solution Tangram Card #2

Solutions for silhouette outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams,…

Solutions for silhouette outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Birds Silhouette Solution Tangram Card

Solutions for silhouette outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from…

Solutions for silhouette outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Boats Silhouette Solution Tangram Card

Solutions for silhouette outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams,…

Solutions for silhouette outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Buildings Silhouette Solution Tangram Card

Solutions for silhouette outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams,…

Solutions for silhouette outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Fish Silhouette Solution Tangram Card

Solutions for silhouette outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made…

Solutions for silhouette outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Florida Birds Silhouette Solution Tangram Card

Solutions for silhouette outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture,…

Solutions for silhouette outlines of household items (iron, pipe, kettle, cup, candle, hammer) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Household Items Silhouette Solution Tangram Card

Solutions for silhouette outlines of household items (iron, pipe, kettle, cup, candle, hammer) made…

Solutions for silhouette outlines of people (runners) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

People Silhouette Solution Tangram Card

Solutions for silhouette outlines of people (runners) made from tangram pieces. Tangrams, invented by…

Solutions for silhouette outlines of people (runners, dancers) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

People Silhouette Solution Tangram Card #2

Solutions for silhouette outlines of people (runners, dancers) made from tangram pieces. Tangrams, invented…

Solutions for silhouette outlines of people (woman standing, water skier, woman kneeling, man walking) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

People Silhouette Solution Tangram Card #3

Solutions for silhouette outlines of people (woman standing, water skier, woman kneeling, man walking)…

Solutions for silhouette outlines of people (swimmer, reclining man, butler, diver) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

People Silhouette Solution Tangram Card #4

Solutions for silhouette outlines of people (swimmer, reclining man, butler, diver) made from tangram…

Solutions for silhouette outlines of people (ice skater, saint statue, walking man, reclining man) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

People Silhouette Solution Tangram Card #5

Solutions for silhouette outlines of people (ice skater, saint statue, walking man, reclining man) made…

Solutions for silhouette outlines of people (silhouettes of men) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

People Silhouette Solution Tangram Card #6

Solutions for silhouette outlines of people (silhouettes of men) made from tangram pieces. Tangrams,…

Solutions for silhouette outlines of sea animals (sea monster, dolphin, sea turtle, stingray) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Sea Animals Silhouette Solution Tangram Card

Solutions for silhouette outlines of sea animals (sea monster, dolphin, sea turtle, stingray) made from…

Solutions for silhouette outlines of shapes (rectangle, parallelogram, isosceles triangle, double arrow, rhombus, hexagon) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Shapes Silhouette Solution Tangram Card

Solutions for silhouette outlines of shapes (rectangle, parallelogram, isosceles triangle, double arrow,…

Solutions for silhouette outlines of shapes (quadrilateral, hexagon, arrow, pentagon) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Shapes Silhouette Solution Tangram Card #2

Solutions for silhouette outlines of shapes (quadrilateral, hexagon, arrow, pentagon) made from tangram…

Tangram pattern with black pieces and thin white-dotted lines. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Tangram Pattern, Black with Small Dotted Lines

Tangram pattern with black pieces and thin white-dotted lines. Tangrams, invented by the Chinese, are…