Hart Combination Protractor, Rule, and Square

In the early 20th century, some authors of mathematics textbooks and their publishers began to include protractors in the endpapers of the books. They wanted middle and high school students to informally experience geometry through drawing and experiment before moving on to constructing formal geometrical proofs. Walter W. Hart, a professor of mathematics at the University of Wisconsin, went so far as to design a combination protractor and ruler for insertion in the textbooks he authored with professional mathematics textbook author Webster Wells.
By 1921, Hart's protractor was described and illustrated in the text with a cardboard version included for student use. If students lost their protractors, teachers could order replacements from D. C. Heath & Co. for four to five cents each, depending on the quantity ordered. By 1926, Hart was boasting that his invention had anticipated the standards recommended in 1923 by the Mathematical Association of America's National Committee on Mathematical Requirements. This example probably dates from one of Hart's later textbooks.
This paper semicircular protractor is divided by degrees and marked by tens from 10 to 170 degrees in both directions. The letter A is printed in the bottom left corner of the protractor, and B is printed in the bottom right corner of the protractor. Centered under the origin point of the protractor is printed the inventor's mark: COMBINATION PROTRACTOR, RULE, AND SQUARE (/) W. W. HART, UNIVERSITY OF WISCONSIN. A ruler along the top edge is divided to 1/8-inch, and marked by ones from 0 to 5. A ruler along the bottom edge is divided to millimeters and marked by ones from 0 to 12. This protractor was donated by the Brown University mathematics department in 1973. It is notably discolored and stained. See also MA*304722.07.
References: Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts, Tools of American Mathematics Teaching, 1800–2000 (Baltimore: Johns Hopkins University Press, 2008), 176–179, 364–365; Walter Wilson Hart, Junior High School Mathematics, vol. 1 (Boston: D. C. Heath & Co., 1921), vii, 131; Webster Wells and Walter W. Hart, Modern Plane Geometry (Boston: D. C. Heath & Co., 1926), 3, 16; National Committee on Mathematical Requirements, The Reorganization of Mathematics in Secondary Education ([Oberlin, OH]: Mathematical Association of America, 1923), 22. See also Walter Wilson Hart, Progressive Plane and Solid Geometry (Boston: D. C. Heath & Co., 1936), iii–vii, 16–17; Claude H. Ewing and Walter W. Hart, Essential Vocational Mathematics (Boston: D. C. Heath & Co., 1945), 99; and Walter Wilson Hart, Veryl Schult, and Henry Swain, Plane Geometry and Supplements (Boston: D. C. Heath & Co., 1959), 24.
Currently not on view
Object Name
date made
after 1930
Date made
post 1930
Hart, Walter Wilson
Physical Description
paper (overall material)
overall: .1 cm x 13.5 cm x 8.2 cm; 1/32 in x 5 5/16 in x 3 7/32 in
place made
United States: Wisconsin, Madison
ID Number
accession number
catalog number
Education, High School
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History, Kenneth E. Behring Center


Add a comment about this object