# 12 Frustum ... History and Etymology of Math Terms

 Frustum (sometimes spelled frustrum)

 is from the Latin and means "a piece broken off". Mathematically it usually refers to a part of a solid cut off between two parallel planes, as opposed to truncated (not necessarily a cut between parallel planes, as a truncated cone has a base that is not a  circle.). The Indo-European root of frustum is bhreus and is related to cutting, crushing, or pounding. Related words from the same root are fragment, bruise, and possibly brush (from a bundle of cut twigs).

Jeff Miller's web site on the earliest use of math words includes a note on how frequently the term is misspelled as "frustrum".

"This word is commonly misspelled as "frustrum" in, for example, Samuel Johnson's abridged 1843 Edition of his dictionary. The word is spelled correctly in the "Frustum" entry and the "Hydrography" entry in the 1857 Mathematical Dictionary and Cyclopedia of Mathematical Science, but it is misspelled in the entry "Altitude of a Frustrum." The word is misspelled in the 1962 Crescent Dictionary of Mathematics and remains misspelled in the 1989 Webster's New World Dictionary of Mathematics, which is a revision of the Crescent dictionary. The word is also misspelled in at least three places in The History of Mathematics: An Introduction (1988) by David M. Burton.

This has become so common it may almost be considered an alternative spelling. He also has, of course, a notation on the first use of the term in English, "FRUSTUM first appears in English in 1658 in The Garden of Cyrus or the Quincuncial Lozenge, or Net-work Plantations of the Ancients ... Considered by Sir Thomas Brown: "In the parts thereof [plants] we finde..frustums of Archimedes" (OED2)."