The magic circle of circles, first developed by Benjamin Franklin, consists of eight annular rings and a central circle, each ring being divided into eight cells by radii drawn from the centre; there are therefore 65 cells. The number 12 is placed in he center and the consecutive numbers 13 to 75 are placed in the other cells. The properties are: 1) sum of eight numbers in any ring with 2 equals 360, 2) sum of eight numbers in any set of radial rings with 12 is 360, 3) sum of numbers in any four adjoining cells is 180.

Magic Circle of Circles

The magic circle of circles, first developed by Benjamin Franklin, consists of eight annular rings and…

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.

A circle divided into ninths with eight ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with eight ninths shaded.

A circle divided into quarters.

Fraction Pie Divided into Quarters

A circle divided into quarters.

A circle divided into quarters with one quarter separated.

Fraction Pie Divided into Quarters

A circle divided into quarters with one quarter separated.

A circle divided into quarters with one quarter shaded.

Fraction Pie Divided into Quarters

A circle divided into quarters with one quarter shaded.

A circle divided into quarters with two quarters shaded.

Fraction Pie Divided into Quarters

A circle divided into quarters with two quarters shaded.

A circle divided into quarters with two quarters shaded.

Fraction Pie Divided into Quarters

A circle divided into quarters with two quarters shaded.

A circle divided into quarters with three quarters shaded.

Fraction Pie Divided into Quarters

A circle divided into quarters with three quarters shaded.

A circle divided into sevenths.

Fraction Pie Divided into Sevenths

A circle divided into sevenths.

A circle divided into sevenths with one seventh separated.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with one seventh separated.

A circle divided into sevenths with one seventh shaded.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with one seventh shaded.

A circle divided into sevenths with two sevenths shaded.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with two sevenths shaded.

A circle divided into sevenths with three sevenths shaded.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with three sevenths shaded.

A circle divided into sevenths with four sevenths shaded.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with four sevenths shaded.

A circle divided into sevenths with five sevenths shaded.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with five sevenths shaded.

A circle divided into sevenths with six sevenths shaded.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with six sevenths shaded.

A circle divided into sixths.

Fraction Pie Divided into Sixths

A circle divided into sixths.

A circle divided into sixths with one sixth separated.

Fraction Pie Divided into Sixths

A circle divided into sixths with one sixth separated.

A circle divided into sixths with one sixth shaded.

Fraction Pie Divided into Sixths

A circle divided into sixths with one sixth shaded.

A circle divided into sixths with two sixths shaded.

Fraction Pie Divided into Sixths

A circle divided into sixths with two sixths shaded.

A circle divided into sixths with two sixths shaded.

Fraction Pie Divided into Sixths

A circle divided into sixths with two sixths shaded.

A circle divided into sixths with three sixths shaded.

Fraction Pie Divided into Sixths

A circle divided into sixths with three sixths shaded.

A circle divided into sixths with three sixths shaded.

Fraction Pie Divided into Sixths

A circle divided into sixths with three sixths shaded.