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Rectangle divided into 7 sections.

Rectangle Divided Into 7 sections

Rectangle divided into 7 sections.

Rectangle divided into 4 sections.

Rectangle Divided Into 4 sections

Rectangle divided into 4 sections.

Illustrations to show that if two parallel lines are cut by a transversal, the bisectors of the interior angles form a rectangle.

Rectangle Formed When Two Parallel Lines are Cut by a Transversal

Illustrations to show that if two parallel lines are cut by a transversal, the bisectors of the interior…

Illustration showing the golden rectangle. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi.

Golden Rectangle

Illustration showing the golden rectangle. Two quantities are considered to be in the golden ratio if…

An illustration of composite rectangle with lengths a, b, and c with area ac + bc. This illustration represents the product of c(a+b).

Rectangle with Lengths a, b, and c with Areas ac and bc

An illustration of composite rectangle with lengths a, b, and c with area ac + bc. This illustration…

Illustration showing a nesting of 2 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again.

Golden Rectangles

Illustration showing a nesting of 2 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 3 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 3 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 4 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 4 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 5 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 5 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 6 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 6 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 7 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 7 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Golden Rectangles

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two…

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Golden Rectangles

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two…

A square divided evenly by a dotted line.

Divided Square

A square divided evenly by a dotted line.

A square divided evenly by a dotted line, known as the diagonal.

Divided Square

A square divided evenly by a dotted line, known as the diagonal.

Illustration of a square inscribed in a square. The interior square is rotated 45° in relation to the exterior square.

Square Inscribed In A Square

Illustration of a square inscribed in a square. The interior square is rotated 45° in relation to…

Illustration of 12 congruent squares that have the same center. Each square has been rotated 7.5° in relation to the one next to it.

12 Congruent Rotated Squares

Illustration of 12 congruent squares that have the same center. Each square has been rotated 7.5°…

Illustration of 16 congruent squares that have the same center. Each square has been rotated 5.625° in relation to the one next to it.

16 Congruent Rotated Squares

Illustration of 16 congruent squares that have the same center. Each square has been rotated 5.625°…

Illustration of 2 concentric squares whose vertices are connected by line segments.

2 Concentric Squares

Illustration of 2 concentric squares whose vertices are connected by line segments.

Illustration of 2 concentric squares.

2 Concentric Squares

Illustration of 2 concentric squares.

Illustration of 2 concentric squares.

2 Concentric Squares

Illustration of 2 concentric squares.

Illustration of 2 congruent squares that have the same center. One square has been rotated 45° in relation to the other.

2 Congruent Rotated Squares

Illustration of 2 congruent squares that have the same center. One square has been rotated 45° in…

Illustration of 3 concentric squares that are equally spaced.

3 Concentric Squares

Illustration of 3 concentric squares that are equally spaced.

Illustration of 3 congruent squares that have the same center. Each square has been rotated 30° in relation to the one next to it.

3 Congruent Rotated Squares

Illustration of 3 congruent squares that have the same center. Each square has been rotated 30°…

Illustration of 4 concentric squares that are equally spaced.

4 Concentric Squares

Illustration of 4 concentric squares that are equally spaced.

Illustration of 4 congruent squares that have the same center. Each square has been rotated 22.5° in relation to the one next to it.

4 Congruent Rotated Squares

Illustration of 4 congruent squares that have the same center. Each square has been rotated 22.5°…

Illustration of 6 congruent squares that have the same center. Each square has been rotated 15° in relation to the one next to it.

6 Congruent Rotated Squares

Illustration of 6 congruent squares that have the same center. Each square has been rotated 15°…

Illustration of 8 congruent squares that have the same center. Each square has been rotated 11.25° in relation to the one next to it.

8 Congruent Rotated Squares

Illustration of 8 congruent squares that have the same center. Each square has been rotated 11.25°…

Illustration of a square inscribed in a square that is inscribed in another square. Each successive square is rotated 45° in relation to the previous square.

Squares Inscribed In Squares

Illustration of a square inscribed in a square that is inscribed in another square. Each successive…

Illustration of a square inscribed in a square that is inscribed in another square. Each successive square is rotated 45° in relation to the previous square. Diagonals of the largest square are shown.

Squares Inscribed In Squares

Illustration of a square inscribed in a square that is inscribed in another square. Each successive…

Illustration of a square inscribed in a square that is inscribed in another square. Each successive square is rotated 45° in relation to the previous square. Line segments are drawn connecting the vertices of the smallest to the vertices of the largest square.

Squares Inscribed In Squares

Illustration of a square inscribed in a square that is inscribed in another square. Each successive…

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 Outline Tangram Card

Outlines of shapes (rectangle, parallelogram, isosceles triangle, double arrow, rhombus, hexagon) made…

Solutions for 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 Outline Solution Tangram Card

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

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 Tangram Card

Silhouette outlines of shapes (rectangle, parallelogram, isosceles triangle, double arrow, rhombus,…

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,…