Who first used the word "Simplex" to describe the considered geometric figure?
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1$\begingroup$ You might want to ask questions like these at History of Science and Mathematics Stack Exchange. $\endgroup$– JRNCommented Jan 10, 2018 at 4:51
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2 Answers
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According to Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics, the first known occurrence is in Schoute’s Mehrdimensionale Geometrie of 1902.
answered Jan 9, 2018 at 19:48
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3$\begingroup$ Your link actually indicates Schoute’s Mehrdimensionale Geometrie (1902) as the first use of the word simplex in geometry. Prime confine is another word. $\endgroup$ Commented Jan 9, 2018 at 20:08
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4$\begingroup$ quote: I was curious how the word "simplex" came into existence. It was the Dutch mathematician Pieter Hendrik Schoute, who introduced the term "simplex". Schoute argued that the most "simple" geometries are those that have no diagonal. This is true for the equilateral triangle, the tetrahedron and its higher analogues, and that is exactly what is required for this type of representation. Schoute decided that a word like "simplicissmus" was too clumsy and proposed instead the shorter term "simplex". $\endgroup$ Commented Jan 9, 2018 at 20:50
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The earliest references found by Google date back to 1909. W.H. Bussey mentions it in an article from that year, On the tactical problem of Steiner published in the Bulletin of the AMS. Precisely, what he defines to be a simplex is the boundary of what is called a simplex today:
The $l+1$ points of such a set, if taken $l$ at a time, determine a number of $l-1$-spaces whose points constitute a set that may conveniently be called a simplex$^*$ of order $l$. The $l + 1$ points are called vertices.
$^*$*The word is used in geometry of n-dimensions to denote the configuration analogous to the triangle in the plane or the tetrahedron in 3-space.
http://www.ams.org/journals/bull/1909-16-01/S0002-9904-1909-01845-2/S0002-9904-1909-01845-2.pdf
