One Entry from "An Etymological and Historical Math Dictionary"

Still trying to work my way through the middle letters of the alphabet, but given people's ideas about what a dictionary is, I wanted to give another example of how different an entry in such a dictionary might be from the perceived expectations. 
It is written with a focus on the students and teachers of high school mathematics, and hope it will be useful to them, and enjoyable and informative to others. 

A link to the Volumes of published so far are on the right of this blog.

So here is my entry for N-Dimensional, please enjoy.

N- Dimensional The earliest mention of dimensions in mathematics are related to algebra, much like we would today speak of the "degree of a polynomial", more than geometry. Still the association between the dimension of an expression was associated with spacial dimension as early as Robert Recorde's Whetstone of Witte in 1570, "The nomber that doeth amount thereof (3x3x3) hath gotten 3 dimensions, whiche properly belong to a bodie, or sound forme, and therefore it is called a cube, or cubike nomber." This usage persisted in to the middle of the 18th century. In 1843, Arthur Cayley wrote,
"Chapters in the Analytic Geometry of (n) Dimensions,"but despite the title, it seems the work was more about algebra than geometry. Reviews of this (I haven't found the paper yet for a personal reading) suggest that he was still using the term in the way Recorde had used it.

Certainly though, by 1878, the idea of a fourth spacial dimension was being discussed and written about. In that year, B Stewart and P G Tait wrote Unseen Universe, and included, "suppose our (essentially three dimensional) matter to be the mere skin or boundary of an Unseen whose matter has four dimensions. C H Hinton, in the same year(1880) he became the son-in-law of the then Late George Boole, wrote a paper in entitled, What is the Fourth Dimension, he suggested that three dimensional objects might be merely cross-sections of four dimensional objects. He would also began teaching that year in the Upland School in Rutland where Howard Chandler also taught, and was a friend of Edwin Abbot, who would write the classic, Flatland, in 1884, describing a similar relationship between some two dimensional creatures and their three dimensional intersections.

Hinton also tutored his sister-in-law Alice (Alicia) Boole, who went on to independently rediscover many facts about the fourth dimension, such as there were only six regular polytopes (Like Platonic solids for higher dimensions) and demonstrated incredible ability to produce careful illustrations of three-dimensional intersections of these objects. For her work,The University of Groningen honoured her by inviting her to attend the tercentenary celebrations of the university and awarding her an honorary doctorate in 1914. Through her nephew, Geoffrey Taylor, a major figure in physics and wave theory, she met HSM Coxeter in 1930 and they began working together and produced a joint paper. To his friends at Cambridge Coxeter referred to her as his "Aunt Alice".

I have written much more about the incredible progeny of George and Mary Boole, Those Amazing Boole Girls, that you might enjoy.