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Mathematical Treasure: Thomas Jefferson's Octagon

Frank J. Swetz (The Pennsylvania State University)

Thomas Jefferson (1743-1826) was a Founding Father of the United States of America. Principal author of the nation’s Declaration of Independence, he went on to become the country’s third President, a leading statesman and diplomat. However, he was much more than a politician; he was a multi-skilled polymath and a leader in the Enlightenment movement of his time. As a self-trained architect, he promoted a classical style in the buildings he designed. In particular, he seemed fascinated with the geometric and structural features of an octagon. This shape had been employed for centuries in the construction of domes but Jefferson appreciated the functional aspects of the space it enclosed: his tearoom at Monticello was enclosed by three sides of an octagon and his retirement retreat, “Plantation House,” was laid out in the shape of an octagon. Among Jefferson’s architectural notes held by the Massachusetts Historical Society is a geometric construction for obtaining three sides of an octagon given the length of the chord subtending them.

Construction of octagon by Thomas Jefferson

Jefferson’s instructions at the upper right read:

To draw 3 sides of an octagon on the subtense a.b. geometrically.

Bisect it by line d.e.

Take c.a. and lay it off towards d. at f.

On the center f. with radius f.a. describe the quadrant a.g.b.

On the center g. with the radius g.a. describe the arc a.h.i.b.

This arc cuts a.f. and b.f at the angles of the octagon required.

Was Thomas Jefferson correct in his construction?

This image has been obtained through the cooperation of the Massachusetts Historical Society. You may use it in your classroom. For any other use, please contact the Massachusetts Historical Society for permission.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Thomas Jefferson's Octagon," Convergence (April 2016)