Math Words, pg 2

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**Calendar** comes to us from the name of a bookkeeping ledger, and indirectly from the ancient Roman practice of starting each month on a new moon. In the earliest Roman calendars, as in many early societies, the cycle of social events was based on the moon. The date of the new moon would signal a new month and the first day of the month was called the *kalends*. Many official practices would occur on this date. The community would gather to hear the announcement of the dates on which the "nones" (nine days before the full moon), and the "ides"(the full moon) would occur, and then, as now, the people you owed money would come around looking for their due. The money lenders of ancient Rome kept their accounts in a record book and it became known as a *kalendarium*. Eventually, the name was applied to the record of dates that we now call a calendar. The genus of the common Pot Marigold, calendula, is from the same root, seemingly because it was thought to be a cure for menstrual disorders.

You can find an extensive discussion on the history of calendars, including Gregorian, Julian, Egyptian, Mayan, Islamic, Jewish, Persian and more at Several Calendars, by Holger Oertel, which also has a calculator to compare dates in many of these different systems. Thanks to this site I now know my birthday in the Mayan calendar system.

**Compass** Many students wonder why the name of the instrument used to draw circles, and the navigational aide used to find directions share a common name. The origin of both words is from the use of a compass to mark off a length. The Latin word *passus* means step, and a compass was used to mark off equal steps. Later the French extended the meaning to include any act of measuring off by steps. For navigation these steps were often around a circle used to measure the direction from North, and the object used to measure was the magnetic needle and a floating card that marked off equal steps (see degree) around a circle, called a compass card. Eventually the card, needle, and all were addressed with the single word, compass. The English extended the idea to other circular references, and then to a general idea of inclusion or surrounding with words such as encompass and compassion.

In earlier times the mathematical compass was called a "compasses" using the plural, and each leg was considered a compass. It seems the mathematical term made it into English first, "The mathematical instrument so called from 1387. The mariners' directional tool (so called since early 15c.) took the name, perhaps, because it's round and has a point like the mathematical instrument. The word is in most European languages, with a mathematical sense in Romance, a nautical sense in Gmc., and both in Eng. " [from the Online Etymology Dictionary]

**Complementary** The Latin word *complere* means to complete. The *ple* root is the same root that gives us the word plus. Most mathematical uses of complement can be understood from this origin. A complement to an angle is the amount needed to complete a right angle. The "tens complement" of six is four, the amount that is needed to complete a ten. The word compliment, for an expression of praise or admiration, is from the same root. It came from a Spanish term for the gift that was given to repay someone for a favor. The gift that would complete the exchange.

**Composite & Compound** A composite number is one that is a product of other parts, its factors. The word joins the Latin *com* (with) and *ponere* (to put), and literally means put together. ** Compound** is drawn from the same roots and has the same meaning. A compound number is a number with a whole part and a fraction part put together. A composition is so called because it is the putting together of parts or elements to make a whole. Compost in the garden is a mixture of decaying organic matter, and a compote is a fruit cooked in heavy syrup until the fruit and syrup are mixed.

**Convex** comes from the two Latin roots *com* (with) and *vehere* (to carry) and literally means "to bring (carry) together". The word seems to be a variation of "convection" from the same roots. * Vehere* is also the base root in vector, and of course, vehicle. In addition the words wiggle, weight, wagon, wave, and (this is no joke) wacko are all related back to the common root.

According to the OED, the first English use of the word in any mathematical sense seems to be in 1571 in __Pantometria__ by Thomas Digges; "1571 DIGGES Pantom. Pref. Aij, *Manyfolde superficies, playne Conuex and Concaue*. Jeff Miller's website states that :

Convex polygon is found in English in 1852 in an adaptation by Charles Davies of Elements of geometry and trigonometry by Adrien Marie Legendre: "When this proposition is applied to polygons which have re-entrant angles, each re-entrant angle must be regarded as greater than two right angles. But to avoid all ambiguity, we shall henceforth limit our reasoning to polygons with salient angles, which are named convex polygons. Every convex polygon is such, that a straight line, drawn at pleasure, cannot meet the sides of the polygon in more than two points" [University of Michigan Digital Library].

**Data/Datum** Datum is from the Latin *dare*, to give, and literally means that which is given. The word seem to have made its way into English from the Latin translation of Euclids "Data", based on the first word in the Greek text(Greek: Δεδομένα, Dedomena) is a work by Euclid. It deals with the nature and implications of "given" information in geometrical problems. The subject matter is closely related to the first four books of Euclid's Elements. *Wik
Data is technically a plural word, but it has become common, and thus acceptable, to use it in a singular sense; "This data supports my claim".

In the fall of 2005 Ron Dirkse, a friend and colleague from Japan, sent a note to the AP Statistics group with a quote about this usage from John Derbyshire's book, __Prime Obsession __(2003), pg 85.

I once got into a mild controversy with the writer and word-lover William F. Buckley, Jr., about the word "data." Is this a singular word or a plural word? The word originated with the Latin verb, dare, "to give."

From this, by the ordinary processes of Latin grammar, a gerund (that is, a verbal noun) can be formed: datum, meaning "that which is given." From this in turn, you can make a plural: data--"those things that are given." However we are speaking English, not Latin. Plenty of Latin plurals are used as English singulars--agenda, for example. Nobody says "The agenda are prepared." English is our language; if we borrow a word from another tongue, we may do with it as we please.

Having worked with data all my adult life, I know very well what it is. It is a stuff, made up of innumerable tiny particles, indistinguishable one from another--like rice, sand, or grass. This kind of stuff needs to be referred to, in English, with singular verb forms ("The rice is cooked") or measured words. If you want to pluck out one particle and address it, you use a measure word: "A grain of rice." "An item of data." This is, in fact, how people who make a living handling data do speak, by instinct.

Among people whose business is data, nobody ever says "One datum, two data." If people did say this, nobody would understand them. The grammarians, however, still want us to say: "The data are...." I predict they will lose the battle eventually.

Many modern words are drawn from this root. Endow, dose and donation have obvious connections to the give meaning. Less obvious, but still related are the words betray, giving counsel or information to the enemy, and surrender, literally the giving over of weapons. The word die, as in dice, is also from the same root.

**Degree** is the union of the Latin roots *de* (down) and *gradus* (step). *Gradus* is actually a derivative from the Latin root for walk or go. Related terms with the same root are congress (come together), regress (to go back), and, of course, grade. **Degree**, as in steps of an angle, dates back at least to the writings of Chaucer who used the word both in Canterbury Tales (seventy times if I counted correctly) and his work on the astrolabe. According to David Eugene Smith the concept of degree originated with the Greeks, who used the word *moira*.

Here is the first few lines from the introduction to the "Man of Laws Tale" where degree is used geometrically (or astronomically)...

Oure hooste saugh wel that the brighte sonneThe reference to phebus is for Phoebus Apollo, the sun.. and note the referral to the shadow being the same length as the tree that cast it indicating the 45

The ark of his artificial day hath ronne

The ferthe part, and half an houre and moore,

And though he were nat depe ystert in loore, He wiste it was the eightetethe day

Of aprill, that is messager to may;

And saugh wel that the shadwe of every tree

Was as in lengthe the same quantitee

That was the body erect that caused it.

And therfore by the shadwe he took his wit

That phebus, which that shoon so clere and brighte,

Degrees was fyve and fourty clombe on highte;

And for that day, as in that latitude,

It was ten of the clokke, he gan conclude,

And sodeynly he plighte his hors aboute.

Lordynges, quod he, I warne yow, al this route,

The fourthe party of this day is gon.

I learned from Russ Rowlett's web page on Units of measurement that in German, Swedish, and other northern European languages the word "grad" means degree

**Diameter** is an apt name for the measure across a circle. The word comes from the union of the Greek roots *dia* (across) and *metros* (to measure). Euclid used diameter in relation to the bisecting chord of a circle and also as the diagonal of a square.

In the study of graphs in discrete mathematics the term diameter is often used for the greatest path length necessary to move between two nodes of a connected graph.

**Dimension** Dimension is used in several different ways in math and science. When we talk about the dimension of a space we mean the number of coordinates needed to identify a point or location in that space. We may speak of a two dimensional plane, or a three dimensional spacial object.

We also use the word to describe the units by which we measure objects. It is the units of dimension that bring reality to a mathematical problem, distinguishing four miles from four feet. The origin of the word is indicative of this measurement theme. Dimension is a weathered and worn version of the union of *dis* (intense/strong) and *meteri* (measure), with a combined meaning of "measure carefully".

**discriminant ** To most algebra students the discriminant is a number related to a quadratic equation that determines the nature of the solutions. The value of the discriminant in a quadratic is given by the expression B^{2} - 4AC. A positive discriminant indicates two real distinct roots, a zero indicates a single real root, and a negative value indicates two complex roots. The actual polynomial discriminant has a denominator which is a power of the leading coefficient, but as the most common use is to determine the number of roots, the (always positive) denominator is ignored.

The discriminant can also be found for higher order Polynomials. The value at all orders can be expressed as the product of the squares of all the differences of any two zeros of the function. A cubic function f(x)= Ax^{3} + Bx^{2}+Cx+D has a discriminant of . For determining whether roots of a cubic are real or non-real complex values, it is again safe to ignore the denominator. If the discriminant is >0 it means that there is one real and two non-real solutions. If D= 0 it means that all the roots are real and at least two are equal. If D<0 then all three roots are real and unequal.

Discriminants also exist for many ideas in math other than the the roots of polynomials. The discriminant of a general second dergree or conic equation, for example, distinguishes if an equation describes an ellipse, parabola, or hyperbola. The term was created in the last half of the 19th century by J J Sylvester, according to the web site of Jeff Miller. "Sylvester used the term in 1852 in the Cambridge and Dublin Mathematical Journal, vol. I, 52. In 1876 George Salmon used discriminant in its modern sense in Mod. Higher Algebra (ed. 3): "The discriminant is equal to the product of the squares of all the differences of the differences of any two roots of the equation" (OED2).

The origin of the word is from the union of *dis*, and the very early Indo-European root *skeri* which referred to separating by sifting, scraping or cutting, through the Greek *krinein* to separate. Descendants of the *skeri* root show up in diverse words today including script, crime, decree, secret, and endocrine.

**Double Dummy** Although it sounds more like the ultimate classroom insult, "double dummy" is the name for a particular technique in the design of an experiment. I had never heard the name until a request was place on the AP Stats newsgroup, and answered by Debra Balm. Here is her response

Double dummy refers to a procedure that is used when the two treatments are so obviously different that it would undermine the whole double blind idea.

For instance, you want to test a medication that is in capsule form to a medication that is a liquid. Obviously, the subject would know what they were getting if just given one of the medications. So each subject receives both treatments with groups structured as follows:

Group One: active capsule, placebo liquid

Group Two: placebo capsule, active liquid

Group Three: placebo capsule, placebo liquid.

**Factor & Factorial** The roots of both these words are in the word fact and its Latin root * facere*, to do. To know the facts, is to know what has been done. The person who does something is then called the factor. In business a factor was once a common term for one who buys or sells for another. Today the word agent is more common. Colonial businesses often employed a person to do various menial tasks, as a factotum, literally one who does everything (today we might call them a "gopher"). Things that were necessary in order to "do something" became factors in the event, and today you may hear a coach say, "Defense was the most important factor in our victory." Factors then became the parts of the whole, and a factory was where they were put together to make a final product. These words run over into the mathematical meanings. The factors are the numbers that are put together (by multiplication) to make the product. Because the product is made up by putting together parts, it is called a composite number.

The word "measure" has often been used in much the same way we now use the word factor. In his __Universal Arithmetick__ Newton distinguishes three kinds of numbers, "integer, fracted, and surd", and defines an integer as "what is measured by Unity." Frederick Emerson's __North American Arithmetic__(1850)says "One number is said to MEASURE another, when it divides it without leaving any remainder." (pg 18) Later it states," A number which divides two or more numbers without a remainder is called their COMMON MEASURE." This is after the definition of factor on page 12, and immediately precedes "A square number is the product of two equal factors" on page 19.

The first use of a multiplication of long strings of successive digits for a specific problem may have been by Euler in solving the questions of derangements. "The Game of Recontre (coincidence), also called the game of treize (thirteen), involves shuffling 13 numbered cards, then dealing them one at a time, counting aloud to 13. If the nth card is dealt when the player says the number 'n,' the dealer wins (this is known in combinatorics as a derangement of 13 objects.). Euler calculates the probability that the dealer will win.

It should be noted that this problem was solved earlier, by P.R. de Montmort, in 1713, though his work was unknown to Euler." (* from a Dartmouth web page*)

In an article entitled, "Calcul de la probabilité dans le jeu de rencontre" published in 1753, Euler wrote.

which is translated by Richard J. Pulskamp as

. Cajori points out that this was probably not intended to be a general notation, but a temporary expedient.

In 1772 A T Vandermonde used [p]^{n} to represent the product of the n factors p(p-1)(p-2)... (p-n+1). With such a notation [p]^{p} would represent what we would now write as p!, but I can imagine this becoming, over time, just [p] (De Morgan would do just such a thing in his 1838 essays on probability). Vandermonde seems to have been the first to consider [p]^{0} and determined it was (as we now do) equal to one. Vandermonde's notation included a method for skipping numbers, so that [p/3]^{n} would indicate p(p-3)(p-6)... (p-3(n-1)).

A few years later, a little known German educator named Johan Bernhard Basedow used a star or asterisk to indicate the factorial, n*. In 1799 Ruffini used a small Greek pi, and in 1811 Gauss upgraded to a capital. Both Gauss' $\Pi (n)$ and Jacobi's \Pi n were regularly used, and were progenitors of the general product symbol now used.

The word factorial is reported to be the creation of Louis François Antoine Arbogast (1759-1803). The symbol now commonly used for factorial seems to have been created by Christian Kramp in 1808 according to a note I found in __Lectures on fundamental concepts of algebra and geometry__ (1911), by John Wesley Young with a note on "The growth of algebraic symbolism" by Ulysses Grant Mitchell. It was in the Note by Mitchell (pg 239) that I found the credit for the symbol to Kramp. Kramp had previously used the word "facultes" for the process, but deferred in favor of Arbogast's term instead. Here is a translation from Jeff Miller's page, "I've named them facultes. Arbogast has proposed the denomination factorial, clearer and more French. I've recognised the advantage of this new term, and adopting its philosophy I congratulate myself of paying homage to the memory of my friend". Both Kramp and Arbogast were working with sequences of products.

In his Dictionary of Curious and Interesting Numbers, David Wells tells the following story: "Augustus de Morgan ... was most upset when the " ! " made its way to England. He wrote:'Among the worst of barberisms is that of introducing symbols which are quite new in matehmatical, but perfectly understood in common, language. Writers have borrowed from teh Germans the abgreviation n! ... which gives their pages the appearance of expressing admiration that 2, 3, 4, etc should be found in mathematical results.'"

The German educator J. D. Basedow used and asterisk or star as a superscript, (4^{*}). Another early symbol (shown below) was also used. Here is the discription of its origin from the web page of Jeff Miller,

An early factorial symbol, was suggested by Rev. Thomas Jarrett (1805-1882) in 1827. It occurs in a paper "On Algebraic Notation" that was printed in 1830 in the Transactions of the Cambridge Philosophical Society and it appears in 1831 in An Essay on Algebraic Development containing the Principal Expansions in Common Algebra, in the Differential and Integral Calculus and in the Calculus of Finite Differences (Cajori vol. 2, pages 69, 75).

I later found a copy of the 1830 paper on Google Books, and here is the way Jarrett presented the notation:

The image below is from the 1889 textbook, __A College Algebra__ by J.M. Taylor of Colgate.

A second image shows that the symbol was still in use even after the textbooks had adopted the "n!" symbol. This image is a note on the top a page on combinations in the 1922 text

Even

I recently found even a later date of the use of the Jarrett symbol. In the Mathematics Teacher for February of 1946 the symbol is used in an article by C. V. Newsome and John F. Randolph in illustrating Newton's power series for Sin(x). The fact that it is done with no comment indicates it must have still been commonly used.I recently encountered an Arabic use of a very similar symbol, that is apparently still current. A note from an AP calculus teacher in February of 2009 indicated that a transfer student from Egypt uses something like ths symbol currently.

There is a more modern extension of the factorial called the **multiple factorial** which allow the symbol to be extended to the idea of multiplying every other number, or every third, etc. For example the use of a double factorial, as in 7!! means multiply 7*5*3*1; and 7!!! would be 7*4*1 (every third multiple). It is important not to confuse these symbols with (7!)! which is the factorial of 7! or 5040!.

A good approximation to n! for large values of n is given by **Stirling's Formula**, which probably ought to be named for De Moivre.

The Factorial can be generalized to the real and complex numbers using the Gamma Function

**Factoring ** (sometimes called "factorizing") for most people who have ever taken high school algebra calls to mind the single, and often dreaded, factoring of quadratic expressions; usually for the purpose of solving a quadratic equation. Many would be surprised to know it is one of the newest methods of solving them. Vera Sanford points out in her "A Short History of Mathematics", (1930) that “In view of the present emphasis given to the solution of quadratic equations by factoring, it is interesting to note that this method was not used until Harriot’s work of 1631. Even in this case, however, the author ignores the factors that give rise to negative roots.” Harriot died in 1621, and like all his books, this one, Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas , was published after his death. An article on Harriot at the Univ of Saint Andrews math history web site says that in his personal writing on solving equations Harriot did use both positive and negative solutions, but his editor, Walter Warner, did not present this in his book. Harriot’s method of factoring may look different to what modern students expect. The image shows a clip from David E Smith’s 1923 History of Mathematics. Harriot writes out a form for each of the possibilities of (a±b)(a±c) with a being the unknown (where we would use x) and then when he needs to factor he picks on one of the forms that match. By separating out the linear coefficient into two parts he is able to break the problem into one of the forms.

For more about the history of solutions to a quadratic you can find my notes here.

Other English words from the "to do" meaning of fact include facility (the ability to do), faction (a group working to do the same thing), facilitate (make easy to do) and faculty.

**Focus** comes from the Latin word for hearth, or fireplace. The first use of focus as a mathematical point, as in an ellipse, appears to have been by Kepler. Perhaps it was the hot sun that inspired the word, or perhaps it was the fact that the hearth was usually the center of activity of a home in the late 1500's. Carl Boyer writes in **A History of Mathematics**, "As the curves (conic sections) are now introduced in textbooks, the foci play a prominent role, yet Apollonius had no names for these points, and he referred to them only indirectly."

**Fractal ** appears to be a very modern term created by Benoit Mandelbrot in an article published in Scientific American magazine around 1975. Mandelbrot discussed his choice of names in __The Fractal Geometry of Nature__. In it he wrote "I coined fractal from the Latin adjective fractus." The *fractus* is a derivative of *frangere*, for broken, which is also the root of fraction

**Ides (of March)** Every month has its ides, but a line from Shakespeare made the "Ides of March" linger in our language long after the others had fallen from use. The ides were the early Roman word for the day of the full moon. Since months began on the new moon, the ides normally occurred near the middle of the month, and the term came to be used for the fifteenth day of the month.

**Index** The use of a number or variable subscript to identify the terms of a sequence or elements of a matrix serves as a way to "point out" particular items. The two in A_{2} is called the index. The origin of the word index comes from that very purpose, to point out. The Greek root *dika* is applied to a wide range of ideas that relate to making one or more items distinct from others by showing, saying, or teaching. To adjudicate is to point out guilt or innocence, and gives us the word judge. The fingers are called digits and the finger with which we most commonly point is called our index finger, a double use of the root. Other related words are dictate, predict, valedictorian, dedicate, condition and the ubiquitous ditto.

**Lemma** Mathematicians use the word lemma to describe a proof which is a preliminary step to a more important or more complete result. The word is directly from the Greek and descended from *lambanein* which meant to receive, take, grasp, or seize. The root is the source of other words like syllable (to take together, to group) and epilepsy (to seize upon).

**Mathematics** The origin of the word mathematics is in the Greek word *manthanein*, to learn. The legend is that it was Pythagorus who created the term. The meaning is preserved today in the word polymath, for a person of great or varied learning. The word is seldom used, but that could be because there are so few people to whom it actually applies.

A note from Sendhil Revuluri to the Teacher2Teacher Discussion group recently included this information from Lewis Thomas

According to Lewis Thomas in "Et Cetera, Et Cetera", as quoted on http://lhall-mac.math.umr.edu/quotes/LThomas2.html:

"The Indo European root for "mathematics', prophesying the whole future of the enterprise, was mendh, meaning learn. Not a root suggesting something natural, lying around in the world waiting to be picked up. On the contrary, a new, ungiven human activity, requiring lots of hard thought and hard work, even possibly, at the end of the day, unattainable. But mendh, learning something, also implies something peculiarly pleasurable for the human mind, with cognates carrying the meaning of awake, alert, wise, and eager."

In __A History of Scientific Ideas__ Charles Singer states in a footnote on the meaning of mathematics, "Greek *mathesis*, 'learning',* mathetes*, 'disciple', so used in the New Testament ... The word mathematics did not enter the English language till the late sixteenth century. The curious plural form is an elliptical expression for 'mathematical sciences' and has no foundation in Greek." Jeff Miller's site has, ".. found in English in 1581 in __Positions, wherein those primitive circumstances be examined, which are necessarie for the training up of children__ by Richard Mulcaster. " The shortened form, "math", used as a word in itself rather than an abbreviation, dates to the early 20th Century. The plural form has remained in the shorter form, "Maths", which is used in many English speaking countries, but in the US the singular "Math" is used.

**One** can be traced back to the Latin *unus* and the Greek *oine* but probably came into English from the German *eine*. In **The Book of Numbers** Conway and Guy point out that numbers related to one include once (one time), only (one like), atone (literally, at one), unanimous (with one voice), and union (one body). Less common are onion and ounce. Many *mono* words are "one" words such as monolith and monopoly, but some are less obvious, like monk (one who lives alone). Solitary is from the Latin *solus* for alone.

From the time of Euclid, one was not generally considered a number. One was considered a unit and numbers were quantities that were composed of units (ones). Even as late as 1585, Simon Stevin called for one to be included with the other integers as a number.

**Pell's Equation** An equation of the form **y ^{2}= Ax^{2}+1**. The name comes from the English mathematician John Pell (1611-1685).

This is one of those many cases in mathematics where the wrong guy gets the credit. It seems that in summarizing some work on the history of the problem, Euler gave credit to Pell when it was Fermat who should have been cited. This was not a judgement call, but apparently a mistake by the great algebraist. In fact Pell had done no more than copy it in his papers from some of Fermat's letters. Fermat had been the first to state that where A is any integer not a square, the equation always has an unlimited number of solutions in integers (x,y)

**Perfect Numbers ** The
perfect numbers are whole numbers that are equal to the
sum of their proper divisors. Six is a perfect number
because 6 = 1+2+3, and was known to the ancients far
into early history. So much has been written, and so
well, that I will suggest the reader try this link to
the topic at University of St. Andrews
Math History website.

**Probability** comes to us from the Old English word Provable and from the Latin *probare*, to prove and the earlier *probus*, goodness or value. The word made its way into mathematics in the early 1700's and may have been introduced by De Moivre. Pascal, a leader in the early development of what we now call probability theory, never used the term. The first textbook about probability was written by Christiaan Huygens (1629-1695), of the Netherlands. The text was *De Ratiociniis in Ludo Aleae *. An English translation can be found here. Today in the law, a probated will is one that is proven (tested in the courts). A person on Probation is given a period of time to prove themselves of value.

**Pronic Numbers** are numbers that are the product of two consecutive integers; 2, 6, 12, 20, ... They are also called
rectangular or ** oblong numbers**. Pronic seems to be a misspelling of *promic*, from the Greek *promekes*, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern
dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history.

**Oblong** is from the Latin *ob* (excessive) + *longus* (long). The word oblong is also commonly used as an alternate name for a rectangle. In his translation of Euclid's "Elements", Sir Thomas Heath translates the Greek word *eteromhkes*[hetero mekes - literally "different lengths"] in Book one, Definition 22 as oblong. . "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an **oblong** that which is right angled but not equilateral...".

Octave 1:2.

fifth 2:3

fourth 3:4

major third 4:5 ... etc

**Regression** is from the Latin roots *re*, back, + *gradus*, to go, and literally translates "to go back". The general meaning, to return to an earlier or more general pattern, fits well with the application to mathematics and statistics. The Oxford English Dictionary indicates that Karl Pearson used the term coefficient of regression in a paper dated 1897.

The first use of the word **regression** is usually credited to Sir Francis Galton. Here is part of a response from Dan Yates to a question to the AP statistics discussion group about the topic

We do know that Sir Francis Galton invented the words 'regression' and 'correlation' and he also gave a definition for r. Although Legendre gets the credit for developing the least-squares method in about 1805, it was Galton who turned regression into a general method for understanding relationships. The term "regression" likely suggested the symbol r for correlation. See page 188 in "The Practice of Statistics," 2nd edition, page 118.

A good reference for Galton and his contributions can be found at Michael Bulmer's online book, "Francis Galton: Pioneer of Heredity and Biometry"

Check out Chapter 5.

Here is another nice link about Galton with info on his life and many areas of activity.

**Science** is from the Latin root *scire*, to know. The earliest origin of the word is realated to cutting or splitting apart. Knowing is, in a sense, the art of being able to seperate ideas from each other. Related terms include conscious, omniscient (all knowing) and less closely related to schizm and schedule.

Although science has been around for a long time, the related term for one who practices science, **scientist**, was only created in the early 19th century. Prior to this time a person who practiced science was addressed as a man of science, or a natural philosopher (see below). In June of 1835 at a meeting of the British Association for the Advancement of Science, the poet Samuel Taylor Coleridge was in attendance. After a speech by William Whewell of Trinity, Coleridge declared that although he was a true philosopher, the term philosopher should not be applied to the association’s members. Whewell responded by coining the word scientist on the spot. He suggested
*by analogy with artist, we may form scientist.
*
Whewell was also frequently in correspondence with Michael Faraday, and created the scientific terms **anode, cathode, and ion**. A letter between the two discussing these three terms is in the Wren Library at Trinity College in Cambridge. I have tried to capture an image below, but the library does not allow flash and the image is taken through the glass case... my apologies that it is not clearer.

In spite of its creation at such a high academic level, the word scientist was not well accepted for a long time. Its eventual acceptance came first in America, but it seems even there it encountered fierce opposition to its formal use well into the Twentieth Century. In __The American Language__ in 1921, H. L. Mencken wrote

The last-namedscientistwas coined by William Whewell, an Englishman, in 1840, [I'm not sure if this date refers to some subsequent publication years after the meeting, but it shows up several places as the "first use"] but was first adopted in America. Despite the fact that Fitzedward Hall and other eminent philologists used it.Despite this fact an academic and ineffective opposition to it still goes on. On the Style Sheet of the Century Magazine it is listed among the "words and phrases to be avoided." It was prohibited by the famous Index Expurgatorius prepared by William Cullen Bryant for the New York Evening Post, and his prohibition is still theoretically in force, but the word is now actually permitted by the Post. The Chicago Daily News Style Book, dated July 1, 1908, also bans it. The use of the word aroused almost incredible opposition in England. So recently as 1890 it was denounced by the London Daily News as "an ignoble Americanism," and according to William Archer it was finally accepted by the English only "at the point of the bayonet."

The term **Natural Philosopher** which scientist replaced had not been around long itself. Prior to the time of Galileo a Philosopher was indifferent to the observed facts, and dealt only with moral and logical theory. Galileo thought that,"The proper object of Philosophy is the great book of nature..." and not the words of other men. Eventually these new students of the "book of nature" became the "Natural Philosophers".

Despite several common assertions to the fact that Whewell coined the term in 1840, the OED lists an earlier use in print, "1834 Q. Rev. LI. 59 Science..loses all traces of unity. A curious illustration of this result may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively. We are informed that this difficulty was felt very oppressively by the members of the British Association for the Advancement of Science, at their meetings..in the last three summers... Philosophers was felt to be too wide and too lofty a term,..; savans was rather assuming,..; some ingenious gentleman proposed that, by analogy with artist, they might form **scientist**, and added that there could be no scruple in making free with this termination when we have such words as sciolist, economist, and atheist; but this was not generally palatable."

William Whewell is buried in Trinity College Chapel in Cambridge, UK. A memorial marker in the chapel is shown here and there is a statue in the ante-chapel

**Similar** Similar comes from the Latin word *similis* (like), and refers to things which share some common characteristic. Similar triangles, for example, share a common shape, but are not necessarily the same size. The word probably dates from the earliest Indo-Europen languages and the sanskrit root *sem* which refers to a quantity of one. Symmetry employs the same root. Related English words include simple (one fold), resemble, simulate, and single. The US Marine Corp slogan, "semper fidelis" (always faithful) uses the Latin compound form *semper* which literally means "once for all".

**Statistics** The word we now use for numerical data and their analysis was originally from the German *statistik* and was used in much the same way we would now use the term "political science". The first appearence of the word in an American dictionary was in 1803. At first statistics did not have to be numbers, but any information about the state of government or the governed. It was derived from the Latin root *status* for position which was from the Greek *statos*, to stand. In the early days of the American republic, *statist* was used as a synonym for statesman. Status is preserved in its original meaning and also is the root of state, as in nations, statue, stay, instant, and literally hundred of other words, including steed and stud (that ought to get your wheels turning).

Here is an explanation of the early devleopment of the term from the MAA's __Historical Modules for the Teaching and Learning of Mathematics__

Statistics, as we know it today, is the branch of mathematics that deals with the collection, organization, and analysis of numerical data. Historically there were two schools of thought. Gottfried A. Auchenwall in 1752 introduced the word “statistik” at Göttingen for “the discipline of statecraft, constitutional history and description of state constitutions” (Pearson, p. 2). We refer to this discipline today as political economy. John Graunt in 1662 published Natural and Political Observations on the London Bills of Mortality and made the first attempt to analyze data. This book was followed with similar work from Sir William Petty, the first insurance mortality table from Edmund Halley, and investigations from Abraham De Moivre. This branch was originally called “Political Arithmetic.” In 1798 Sir John Sinclair borrowed the words “statistics” and “statistik” and applied them to the data and methods of political arithmetic. (Pearson, pp. 2, 8-9) Even though the professors at Göttingen protested, the association of the word “statistics” with numerical data became permanent and is still used.

Bea Lumpkin, in a posting to the Historia Matematica newsgroup, has indicated that some early Egyptian records may be the oldest statistical tables in existance.

What can be claimed for early Egyptian collection and presentation of data is still impressive. For example, the Palermo stone, named for the museum where it is displayed, is one of the earliest (or earliest) historical and statistical records extant. It lists the reigns of kings from c -3100 predynastic to c -2300, 5th dynasty. The record is in tabular form, ruled into rows and columns. The columns are arranged in chronological order, itself a concept not to be taken for granted at this early date. The top row gives the king's name, the middle row events of that year and enumeration of wealth including a biennial count of cattle. The bottom row gives the height of the Nile flood. If the ancients were looking for a pattern in the annual floods, none has been found to date.On the other hand, THE TRIUMPH OF NUMBERS How Counting Shaped Modern Life, a recent book by I. Bernard Cohen suggests that, "Statistical analysis debuted with 17th century Englishman John Gaunt, who analyzed births and deaths during London’s plague years and derived a fairly accurate estimate of the city’s population." I guess it all depends how you define your terms.

On Palermo Stone, see Sir Alan Gardiner, EGYPT OF THE PHARAOHS, Oxford U. Press, 1963, 62-4

Barry J. Kemp, ANCIENT EGYPT, ANATOMY OF A CIVILIZATION, Rutledge 1993, 23

In the fall of 2003 a post to the APStats electronic discussion list pointed out that the Japanese word for statistics, *toukei*, sounds very much like the name of the famous American statistician John Tukey. Ron Dirkse, who teaches at the American School in Japan, added that "according to a native speaker the tou
means something like 'put together' and the kei is 'measure, calculate or
total'. She thought it was interesting that there was a Tukey famous in
statistics, but this word pre-dates him by a lot."

**Supplement** The supplement of an angle is the angle that must be added to "fill up" a semi-circle. The *sup* root is a variation of the common *sub* for below or under. The *ple* is the same root that gives us the math word plus for "to increase or add to" something. Together they suggest the addition of something to fill the "low" amount. Several other English words are formed from the same roots. Supply is an alternative of the same word. The word supplicate, meaning beg or implore, is from one who needs to be supplied. Supple, for limber, is perhaps an early version of "beggars can't be choosers"; those who need should remain flexible.

**Trajectory** The trajectory of a particle or a point on a plane is the set of points which determine its path. The root is from the Latin *trajectus* which unites *trans* for across, and *ject* for throw, with a literal meaning of "to throw across." Other modern words drawing on the *ject* root include project (to throw forward) and adjective (to throw to) among a host of others.

**Two** is descended from the Greek root *dyo* and the Latin root *duo* through the Old English *twa*. Early languages often had both feminine and masculine forms for two and so there are abundant and diverse roots related to "two-ness". Many "two" words use the Greek root *bi*; biannual, binary, biscuit, and biceps are examples. Others come from the Old English *twa*, such as between, twilight, twist, and twin. From *duo* we get dual, duet, dubious (of two minds), duplex (two layers) and double. The Latin *di* gives us diploma (two papers) and dihedral. The earlier Greek *dyo* produces dyad, composed of two parts. When *am* precedes *bi*, as in ambivalent, it means "either of two".

The word *didymous* is Greek for twin, and is used in scientific terms to represent things which occur in pairs. Students of the bible may remember that didymous is also the nickname of the disciple Thomas (John 11:16). Thomas itself is from the old Aramaic word for twin, *t'oma*, which was also used by the Greeks and later made its way into Latin.

In Henry B. Fine's *The Number System of Algebra*, 1903, he points out that the name for two often was drawn from dual body parts, such as eyes, ears, or wings. "'Two" in Chinese is a word meaning 'ears,' in Thibet 'wing" in Hottnetot 'hand'". It would seem that such a system would be thwarted by the difficulty of finding body parts to represent three and four.