Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Construction Of Line Equal To Arc

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Illustration showing a line with a midpoint drawn from a given exterior point to a given circumference.

Midpoint of Straight Line Drawn From an Exterior point to Circumference

Illustration showing a line with a midpoint drawn from a given exterior point to a given circumference.

Illustration showing a line that remains parallel to a given line, and touches at one end a given circumference.

Straight Line Moving to Two circles

Illustration showing a line that remains parallel to a given line, and touches at one end a given circumference.

Illustration showing a line that moves so that its ends constantly touch two fixed lines which are perpendicular to each other. Locus of the midpoint.

Circle Made by Ends of a Line Touching Two Fixed Lines Perpendicular to Each Other

Illustration showing a line that moves so that its ends constantly touch two fixed lines which are perpendicular…

A circle with many tangent and secant lines passing through it.

Lines

A circle with many tangent and secant lines passing through it.

Labeled shapes showing various measures of form.

Measures of Form

Labeled shapes showing various measures of form.

This Medieval Tile circle pattern is a stained glass design. It the oldest process of fitting together pieces of colored glass in a mosaic style.

Medieval Tile Pattern

This Medieval Tile circle pattern is a stained glass design. It the oldest process of fitting together…

This medieval tile pattern is a stained glass design. It the oldest process of fitting together pieces of colored glass in a mosaic style.

Medieval Tile Pattern

This medieval tile pattern is a stained glass design. It the oldest process of fitting together pieces…

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…

Regular nonagon inscribed in a circle.

Nonagon Inscribed in a Circle

Regular nonagon inscribed in a circle.

"An oblique cone connecting two parallel pipes of different diameters... the true size of the base is not given in the top view and must be revolved until parallel to H."—French, 1911

Oblique Cone by Triangulation Connecting to Two Parallel Pipes of Different Diameters

"An oblique cone connecting two parallel pipes of different diameters... the true size of the base is…

A development or rolled out oblique cone using triangulation. The method of triangulation is done by creating series of triangles respect to the base.

Development of Oblique Cone by Triangulation

A development or rolled out oblique cone using triangulation. The method of triangulation is done by…

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…

the octant of the wave surface cuts each coordinate plane in a circle and an ellipse.

Octant of Wave Surface

the octant of the wave surface cuts each coordinate plane in a circle and an ellipse.

Oval with dotted vertical and horizontal lines that are lines of symmetry.

Lines of Symmetry, Oval With

Oval with dotted vertical and horizontal lines that are lines of symmetry.

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and from the center C erect the perpendicular CD. Bisect the radius AC at E; with E as center, and DE as radius, draw the arc DE, and the straight line DF is the length of the side of the pentagon."

Construction Of A Pentagon Inscribed In A Circle

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and…

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular to and half the length of AB; join A and C prolonged to D; with C as center and CB as radius, draw the arc BD; then the chord BB is the radius of the circle circumscribing the pentagon. With A and B as centers, and BD as radius, draw the cross O in the center."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular…

Regular pentagon inscribed in a circle, circumscribed about a circle.

Pentagon Inscribed & Circumscribed in Circles

Regular pentagon inscribed in a circle, circumscribed about a circle.

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a circle circumscribed about a pentagon. In this illustration, the pentagon is not regular (the lengths of the sides are not equal).

Cyclic Pentagon

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a…

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found using Ptolemy's theorem. The lines that are bolded form a quadrilateral. Ptolemy's theorem says the square of b equals the sum of a squared and ab, which in turn gives the golden ratio.

Golden Ratio In A Pentagon

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found…

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon. Construction lines shown.

Pentagon Inscribed in Circle by Construction

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon. Construction…

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed about a circle.

Regular Pentagon With Circle Inscribed

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed…

Illustration of a circle with center O and diameters AB and CD perpendicular to each other.

Circle With 2 Perpendicular Diameters

Illustration of a circle with center O and diameters AB and CD perpendicular to each other.

A circle divided into eighths.

Fraction Pie Divided into Eighths

A circle divided into eighths.

A circle divided into eighths with one eighth separated.

Fraction Pie Divided into Eighths

A circle divided into eighths with one eighth separated.

A circle divided into eighths with one eighth shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with one eighth shaded.

A circle divided into eighths with two eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with two eighths shaded.

A circle divided into eighths with three eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with three eighths shaded.

A circle divided into eighths with four eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with four eighths shaded.

A circle divided into eighths with four eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with four eighths shaded.

A circle divided into eighths with five eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with five eighths shaded.

A circle divided into eighths with six eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with six eighths shaded.

A circle divided into eighths with seven eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with seven eighths shaded.

A circle divided into elevenths.

Fraction Pie Divided into Elevenths

A circle divided into elevenths.

A circle divided into elevenths with one eleventh separated.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with one eleventh separated.

A circle divided into elevenths with one eleventh shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with one eleventh shaded.

A circle divided into elevenths with two elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with two elevenths shaded.

A circle divided into elevenths with three elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with three elevenths shaded.

A circle divided into elevenths with four elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with four elevenths shaded.

A circle divided into elevenths with five elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with five elevenths shaded.

A circle divided into elevenths with six elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with six elevenths shaded.

A circle divided into elevenths with seven elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with seven elevenths shaded.

A circle divided into elevenths with eight elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with eight elevenths shaded.

A circle divided into elevenths with nine elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with nine elevenths shaded.

A circle divided into elevenths with ten elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with ten elevenths shaded.

A circle divided into fifths.

Fraction Pie Divided into Fifths

A circle divided into fifths.

A circle divided into fifths with one fifth separated.

Fraction Pie Divided into Fifths

A circle divided into fifths with one fifth separated.

A circle divided into fifths with one fifth shaded.

Fraction Pie Divided into Fifths

A circle divided into fifths with one fifth shaded.

A circle divided into fifths with two fifths shaded.

Fraction Pie Divided into Fifths

A circle divided into fifths with two fifths shaded.

A circle divided into fifths with three fifths shaded.

Fraction Pie Divided into Fifths

A circle divided into fifths with three fifths shaded.

A circle divided into fifths with four fifths shaded.

Fraction Pie Divided into Fifths

A circle divided into fifths with four fifths shaded.

A circle divided into ninths.

Fraction Pie Divided into Ninths

A circle divided into ninths.

A circle divided into ninths with one ninth separated.

Fraction Pie Divided into Ninths

A circle divided into ninths with one ninth separated.

A circle divided into ninths with one ninth shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with one ninth shaded.

A circle divided into ninths with two ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with two ninths shaded.

A circle divided into ninths with three ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with three ninths shaded.

A circle divided into ninths with four ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with four ninths shaded.

A circle divided into ninths with five ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with five ninths shaded.

A circle divided into ninths with six ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with six ninths shaded.

A circle divided into ninths with seven ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with seven ninths shaded.