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### Etymology of the Word Tessellation

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Date: 11/05/2001 at 07:30:13
From: Cindy Denning
Subject: Tessellations

Are tessellations related to the "tesseract" in Madeleine L'Engle's
_Wrinkle in Time_ series?  If so, can you tell me how?
```

```
Date: 11/05/2001 at 08:14:56
From: Doctor Sarah
Subject: Re: Tessellations

Hi Cindy - thanks for writing to Dr. Math.

Interesting question! Here's what Steven Schwartzman has to say about
the etymologies of the two words in his _The Words of Mathematics - An
Etymological Dictionary of Mathematical Terms Used in English_
(Mathematical Association of America).

tessellate (verb), tessellation (noun):

from Latin tessera "a square tablet" or "a die used for gambling."
Latin tessera may have been borrowed from Greek tessares, meaning
"four," since a square tile has four sides. The diminutive of tessera
was tessella, a small, square piece of stone or a cubical tile used in
mosaics. Since a mosaic extends over a given area without leaving any
region uncovered, the geometric meaning of the word tessellate is "to
cover the plane with a pattern in such a way as to leave no region
uncovered." By extension, space or hyperspace may also be tessellated.

tesseract (noun):

the first component is from Greek tessares "four." The second
component is from Greek aktis "ray of light." A tesseract is a four-
dimensional hypercube. In other words, a tesseract is to four
dimensions what a cube is to three and a square is to two. In the same
way that a cube can be projected onto a plane, a tesseract can be
projected (as if with rays of light) onto space; we can visualize the
three-dimensional projection of the four-dimensional tesseract, even
if we can't see the tesseract itself.

- Doctor Sarah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Definitions
High School Geometry
High School Higher-Dimensional Geometry
High School Symmetry/Tessellations

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