Illustration of a regular nonagon inscribed in a circle. This could also be described as a circle circumscribed about a regular nonagon.

Nonagon Inscribed in a Circle

Illustration of a regular nonagon inscribed in a circle. This could also be described as a circle circumscribed…

Development and top completion exercise problem of the cone by dividing the base into equal parts and creating an arc to revolve the sides of the plane.

Development Exercise of Cone

Development and top completion exercise problem of the cone by dividing the base into equal parts and…

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones by using series of cone development.

Development Exercise of Flange and Hood Cones

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones…

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing area.

Development Exercise of Cylinder

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing…

A development, or rolled out, cone where the point A is the meeting point for the sides. The development is drawn by drawing the arc by using a compass.

Development of Cone

A development, or rolled out, cone where the point A is the meeting point for the sides. The development…

A rolled out, or development, of the cylinder. The development is created by drawing the top curve with the dashed line where the folds are.

Development of Cylinder

A rolled out, or development, of the cylinder. The development is created by drawing the top curve with…

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at point E for reference, and the shape of the sides are by using the reference point.

Development of Rectangle Pyramid

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at…

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom of each triangles to guide the straight lines. The triangle ABC is the base of the pyramid. When folded, the pyramid will form from the image.

Development of Triangle Pyramid

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom…

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular diagram is the main cylindrical body with a circle inside it for the other cylinder. The smaller development is the intersected cylinder. This is commonly used to illustrate pipes.

Development of Two Intersecting Cylinder

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular…

Illustration of 12 equilateral triangles inscribed in an equilateral dodecagon. Each vertex of the dodecagon contains a vertex of a triangle.

12 Triangles Inscribed In A Dodecagon

Illustration of 12 equilateral triangles inscribed in an equilateral dodecagon. Each vertex of the dodecagon…

Illustration of 3 squares inscribed in an regular dodecagon. Each vertex of the dodecagon is also a vertex of one of the squares.

3 Square Inscribed In A Dodecagon

Illustration of 3 squares inscribed in an regular dodecagon. Each vertex of the dodecagon is also a…

Illustration of a regular hexagon and an equilateral triangle inscribed in a regular dodecagon. This could also be described as an equilateral triangle inscribed in a regular hexagon, which is inscribed in a regular dodecagon.

Hexagon And Triangle Inscribed In A Dodecagon

Illustration of a regular hexagon and an equilateral triangle inscribed in a regular dodecagon. This…

Illustration of a regular hexagon inscribed in a regular dodecagon. This could also be described as a regular dodecagon circumscribed about a regular hexagon.

Hexagon Inscribed In A Dodecagon

Illustration of a regular hexagon inscribed in a regular dodecagon. This could also be described as…

Illustration of a square circumscribed about a regular dodecagon. This could also be described as a dodecagon inscribed in a square.

Square Circumscribed About A Dodecagon

Illustration of a square circumscribed about a regular dodecagon. This could also be described as a…

Illustration of a square inscribed in an regular dodecagon.  This could also be described as a regular dodecagon circumscribed about a square.

Square Inscribed In A Dodecagon

Illustration of a square inscribed in an regular dodecagon. This could also be described as a regular…

Illustration of 2 squares; one inscribed in a regular dodecagon and the other circumscribed about the same dodecagon.

Squares Inscribed and Circumscribed About a Regular Dodecagon

Illustration of 2 squares; one inscribed in a regular dodecagon and the other circumscribed about the…

Illustration of an equilateral triangle inscribed in an equilateral dodecagon. This could also be described as a dodecagon circumscribed about an equilateral triangle.

Triangle Inscribed In A Dodecagon

Illustration of an equilateral triangle inscribed in an equilateral dodecagon. This could also be described…

A development or rolled out image exercise problem of the dome and finding the true shape of the hip, or edge, of the dome by using projections or with dividers.

Development Exercise of Dome and True Shape of Hip

A development or rolled out image exercise problem of the dome and finding the true shape of the hip,…

Illustration of a rhombus circumscribed about an ellipse. This could also be described as an ellipse inscribed in a rhombus.

Rhombus Circumscribed About an Ellipse

Illustration of a rhombus circumscribed about an ellipse. This could also be described as an ellipse…

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been rotated 12° in relation to the one next to it. The outer vertices are connected with a smoother curve to form a circle. Hence, the circle is circumscribed about the triangles.

10 Congruent Rotated Equilateral Triangles

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been rotated 12° in relation to the one next to it.

10 Congruent Rotated Equilateral Triangles

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 20 congruent equilateral triangles that have the same center. Each triangle has been rotated 6° in relation to the one next to it.

20 Congruent Rotated Equilateral Triangles

Illustration of 20 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 5 congruent equilateral triangles that have the same center. Each triangle has been rotated 24° in relation to the one next to it.

5 Congruent Rotated Equilateral Triangles

Illustration of 5 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of a circle inscribed in a regular nonagon. This could also be described as a regular nonagon circumscribed about a circle.

Circle Inscribed in a Nonagon

Illustration of a circle inscribed in a regular nonagon. This could also be described as a regular nonagon…

Illustration of an equilateral triangle inscribed in a regular nonagon. This could also be described as a a regular nonagon circumscribed about an equilateral triangle.

Triangle Inscribed in a Nonagon

Illustration of an equilateral triangle inscribed in a regular nonagon. This could also be described…

A problem exercise creating a stretched out or developed image of the octagonal light shade by using the hexagonal pyramid development method.

Development Exercise of Octagonal Light Shade

A problem exercise creating a stretched out or developed image of the octagonal light shade by using…

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the true shape of hip rafter by using projections or dividers.

Development Exercise of Octagonal Roof and True Shape of Rafter

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the…

Illustration of 2 concentric pentagons.

2 Concentric Pentagons

Illustration of 2 concentric pentagons.

Illustration of 2 concentric pentagons.

2 Concentric Pentagons

Illustration of 2 concentric pentagons.

Illustration of 2 regular congruent pentagons that have the same center. One pentagon has been rotated 36° in relation to the other.

2 Congruent Rotated Pentagons

Illustration of 2 regular congruent pentagons that have the same center. One pentagon has been rotated…

Illustration of 3 concentric pentagons that are equally spaced.

3 Concentric Pentagons

Illustration of 3 concentric pentagons that are equally spaced.

Illustration of 4 concentric pentagons that are equally spaced.

4 Concentric Pentagons

Illustration of 4 concentric pentagons that are equally spaced.

Illustration of 4 regular congruent pentagons that have the same center. Each pentagon has been rotated 18° in relation to the one next to it.

4 Congruent Rotated Pentagons

Illustration of 4 regular congruent pentagons that have the same center. Each pentagon has been rotated…

Illustration of 8 regular congruent pentagons that have the same center. Each pentagon has been rotated 9° in relation to the one next to it.

8 Congruent Rotated Pentagons

Illustration of 8 regular congruent pentagons that have the same center. Each pentagon has been rotated…

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development, or stretched out, of the image by creating edges at equal lengths, and revolving the sides.

Development Exercise of Hexagonal Pyramid

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development,…

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal pyramid. The stretched out image is created by drawing an arc with the perimeter of the base stepped off to create an intersection point.

Development Exercise of Oblique Hexagonal Pyramid

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal…

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled out image, of the pyramid.

Development Exercise of Pentagonal Pyramid

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled…

The problem exercise in completing the top view and creating the development, or rolled out, image of the pentagonal pyramid.

Development Exercise of Pentagonal Pyramid

The problem exercise in completing the top view and creating the development, or rolled out, image of…

Illustration of a pentagon with sides measuring 6 2/3', 4 1/2', 5 1/3', 4 3/4', and 9 5/12'.

Pentagon With Sides Labeled

Illustration of a pentagon with sides measuring 6 2/3', 4 1/2', 5 1/3', 4 3/4', and 9 5/12'.

An illustration of a square and triangles within the square. This is an example of a problem that can be used to fine the distances of two inaccessible objects without measuring elevation and whether on a horizontal plane or not.

Square

An illustration of a square and triangles within the square. This is an example of a problem that can…

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…

The exercise problem of creating a three piece elbow development or rolled out image of the cylinder using projections or with dividers.

Development Exercise of Cylinder using Three Piece Elbow

The exercise problem of creating a three piece elbow development or rolled out image of the cylinder…

Illustration of a regular nonagon inscribed in an equilateral triangle. This could also be described as an equilateral triangle circumscribed about a regular nonagon.

Nonagon Inscribed in a Triangle

Illustration of a regular nonagon inscribed in an equilateral triangle. This could also be described…

Exercise problem to develop, or rolled out, image of the triangular pyramid by creating an equal length of the edges of each triangle.

Development Exercise of Triangular Pyramid

Exercise problem to develop, or rolled out, image of the triangular pyramid by creating an equal length…