Sliding Chart for Trigonometry - Triangulator


This small sliding chart for teaching trigonometry shows formulae used to calculate angles, sides, area, sines, cosines and tangents in a right triangle. A plastic card slides in a sleeve that shows a right triangle on each side of it. Windows in the sleeve reveal letters of sides and/or angles of the triangle that are known, as well as a question mark for the side or angle to be found. Another window shows a formula that allows calculation of the unknown from the known. Thirty-two different formulae are listed on the two sides of the card.

One side of the chart has the mark: “Makes TRIGONOMETRY Easy”. It and the slide also are marked: “TRIANGULATOR” (/) P.O. BOX 4660 (/) WASHINGTON, D. C. The other side of the chart is marked: U. S. Pat. 2166372.

The chart and a pink leaflet giving instructions (1986.0441.02) fit in a small tan envelope. George E. Roeder copyrighted the term triangulator in 1936. He applied for a patent on June 16, 1938, and was granted U.S. Patent 2166372 July 18, 1939. The object is very similar but not identical to the patent drawing. Roeder (1895-1954) was born in Germany, became a naturalized U.S. citizen, was working as an instrument maker in Washington, D.C. in 1940, and would die in Buffalo, New York. An ad for the Triangulator appeared in the Hartford Courant in 1942. Advertisements for the instrument appeared in Popular Science as late as 1959, although by then it was distributed from Buffalo, New York.

According to the accession file, the donor had the Triangulator when he was an apprentice mechanic in about 1954.


Accession file.

George E. Roeder, “Formula-Finding Device,” U.S. Patent 2166372, July 18, 1939.

[Advertisement], Hartford Courant, August 9, 1942, p. 8. The Triangulator sold for 75 cents.

[Advertisement], Popular Science, 175, #6, December, 1959, p. 47.

Date Made: ca 1954

Maker: Roeder, George E.

Location: Currently not on view

Place Made: United States: District of Columbia, Washington

Subject: Mathematics


See more items in: Medicine and Science: Mathematics, Trigonometry, Science & Mathematics


Exhibition Location:

Credit Line: Gift of George A. Norton

Data Source: National Museum of American History

Id Number: 1986.0441.01Catalog Number: 1986.0441.01Accession Number: 1986.0441

Object Name: calculating instrument, trigonometric

Physical Description: plastic (instrument material)paper (envelope material)Measurements: overall: .1 cm x 13.8 cm x 6.5 cm; 1/32 in x 5 7/16 in x 2 9/16 in


Record Id: nmah_1134187

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.