Sources page biographical material

6.C. CURVES OF CONSTANT WIDTH
Such curves play an essential role in some ways to drill a square hole, etc.
L. Euler. Introductio in Analysin Infinitorum. Bousquet, Lausanne, 1748. Vol. 2, chap. XV, esp. § 355, p. 190 & Tab. XVII, fig. 71. = Introduction to the Analysis of the Infinite; trans. by John D. Blanton; Springer, NY, 1988-1990; Book II, chap. XV: Concerning curves with one or several diameters, pp. 212-225, esp. § 355, p. 221 & fig. 71, p. 481. This doesn't refer to constant width, but fig. 71 looks very like a Reuleaux triangle.

L. Euler. De curvis triangularibus. (Acta Acad. Petropol. 2 (1778(1781)) 3 30) = Opera Omnia (1) 28 (1955) 298 321. Discusses triangular versions.

M. E. Barbier. Note sur le problème de l'aiguille et jeu du joint couvert. J. Math. pures appl. (2) 5 (1860) 273 286. Mentions that perimeter = π * width.

F. Reuleaux. Theoretische Kinematik; Vieweg, Braunschweig, 1875. Translated: The Kinematics of Machinery. Macmillan, 1876; Dover, 1964. Pp. 129 147.

Gardner D. Hiscox. Mechanical Appliances Mechanical Movements and Novelties of Construction. A second volume to accompany his previous Mechanical Movements, Powers and Devices. Norman W. Henley Publishing Co, NY, (1904), 2nd ed., 1910.

Item 642: Turning a square by circular motion, p. 247. Plain face, with four pins forming a centred square, is turned by the lathe. A triangular follower is against the face, so it is moved in and out as a pin moves against it. This motion is conveyed by levers to the tool which moves in and out against the work which is driven by the same lathe.

Item 681: Geometrical boring and routing chuck, pp. 257-258. Shows it can make rectangles, triangles, stars, etc. No explanation of how it works.

Item 903A: Auger for boring square holes, pp. 353-354. Uses two parallel rotating cutting wheels.

H. J. Watts. US Patents 1,241,175 7 -- Floating tool chuck; Drill or boring member; Floating tool chuck. Applied: 30 Nov 1915; 1 Nov 1916; 22 Nov 1916; all patented: 25 Sep 1917. 2 + 1, 2 + 1, 4 + 1 pp + pp diagrams. Devices for drilling square holes based on the Reuleaux triangle.

T. Bonnesen & W. Fenchel. Theorie der konvexen Körper. Berlin, 1934; reprinted by Chelsea, 1971. Chap. 15: Körper konstanter Breite, pp. 127 141. Surveys such curves with references to the source material.

G. D. Chakerian & H. Groemer. Convex bodies of constant width. In: Convexity and Its Applications; ed. by Peter M. Gruber & Jörg M. Wills; Birkhäuser, Boston, 1983. Pp. 49 96. (??NYS -- cited in MM 60:3 (1987) 139.) Bibliography of some 250 items since 1930.