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The Mis-Named Stutterer

During the War of the League of Cambrai, the French army invaded the city of Breschia in the Lombardy area of Italy.  The city defended itself for seven days, but when the French broke through they went on a rampage of revenge and slaughter that killed off over forty-five thousand of the cities residents. 

It was on this day (Feb 19) in 1512 that one of those French Soldiers slashed a twelve year old boy across the face with a sabre disfiguring the childs palete to the point that he acquired the nickname "Tartaglia", the stutterer, because of his difficulty speaking. Tartaglia went on to be a very good mathematician and is remembered mostly today for his conflict with the great Cardano, but when his birth name is given at all, it seems it may be mostly given wrong.

Tartaglia's father died when he was only six years old, and it seems that the only recorded name for him was Michiel di Bressa, refering to his being from bressia (today Brescia). In this period in Italian History it was not unusual for people not to have a "family" name but to use such a topological reference; think of Leonardo da Vinci, for example. If you search Tartaglia on the internet you will find his name given, most often, as Niccolo (sometimes Niccoli) Fontana. That's what it says on Wikipedia, and even at the usually very reliable St Andrews Math History web page. That's what I thought was true for most of the years I taught, and so some of my student's (the ones who actually listended to my little history asides in math class) may have thought so too.

A while back I came across a nice article by Friedrich Katscher at the MAA’s Convergence web site that explained part of the confusion, but not all.   Professor Katscher even offers to pay big money ($1000 US) to anyone who can find any document where Tartaglia called himself Fontana, base on some pretty extensive research at Austrian an Italian reference libraries.  The story of how that mistake might have been made is pretty credible to me.  Three days before his death on December 13, 1557, Tartaglia appointed his brother as his legal heir. His brother went by the name of John Peter (Zuampiero) Fontana.  No reason is given for the brother having adopted the name Fontana, but afterwards, historians assumed this was in fact the name of the long dead father, and Tartaglia as well.  

The Professor stated that in all his Italian works, he only used, "Tartalea or Tartaglia", two variants of the nickname he acquired as a child.  I would imagine if he assumed this as his personal name, he had grown past the severe speaking problem that earned him the nickname, but have no evidence of that.  " I own facsimile editions of two of his works and even the original of his first book, La Nova Scientia, edition  of 1550. Not only in all titles of his works you find the author Nicolo Tartaglia (before 1550 Tartalea) but he described also conversations he had, and published correspondences. In every talk, and in every correspondence he was always called Nicolo Tartalea or Tartaglia and he himself signed only Nicolo Tartalea or Tartaglia."

Additional compelling proof that Nicolo did not go by the name Fontana is given by the fact that, "The notary public Rocho de Benedetti had the duty to write the proper name of the decedent. But although he must have noticed that his brother had the family name Fontana he called the testator Nicolo Tartaia or Tartalea, and not Fontana. The notary also did not call his father Michele Fontana but in Italian Michiel di Bressa... "  

As far as the use of Niccolo (Niccoli) as often used (Strangely the St Andrews site spells the name with one c in one place and two in another.) , the Professor merely proclaims "The spelling of his given name, Niccolò, found in many papers and books, even Italian ones, is wrong!" 

The actual MAA posting is here.

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Nuts, Again

It was on a Sunday twelve years ago today that the last original Peanuts hit the papers.  Snoopy, atop his
doghouse at the typewriter, ended the run of a comic that had been there for a half-century.  It happened, by chance, on the morning following the death of creator Charles Schulz. 

I guess it is a day for nuts.  Stockard Channing and Jerry Springer were both born on this day in 1944... and at least one of them is nuts.  About 25 years before that, Tennesse Earnie Ford was born.  He described himself as a pea-picker rather than a peanut, but close enough. 

And in 1920, the National Negro League was founded by a nut from Chicago named Rube Foster.  Rube was perhaps the greatest negro pitcher of the period...and he was the founder of the longest lasting of the negro leagues.  When he started the league,he actually owned the contract of every player in the league.  He managed to get the use of Mack Park in Detroit for one of his charter teams, the Detroit Stars.  Mack Park was located about four miles from downtown Detroit at the corner of Fairview Ave. and Mack Ave, hence the name.  Although the area was predominantly German immigrants, the Mack trolley made it easy for supporters to make it out to the park from the black areas of the city. 

And then one day, as the story is told by Wikipedia, "In July 1929, the Kansas City Monarchs were in Detroit to play a doubleheader with the Stars. Two days of heavy rain left the ball field with standing water and threatened to postpone the game. Roesink,(the Grand Rapids hat maker who owned the park) working with the grounds crew, ordered gasoline to be spread on the field for eventual ignition to dry out the field and save the game from cancellation. (You know that was nuts..) After dispersing as much gasoline as they needed, the grounds crew stored the spare cans below the wooden bleachers(Uh oh... probably not a good idea). It is thought that a discarded cigarette butt accidentally ignited the gasoline on the field. Flames quickly spread to the storage area, resulting in a raging fire that engulfed the wooden framework of the stadium." (how totally unexpected..... if you are nuts.)

After the fire, Mack Park was rebuilt and managed to provide a site for HS baseball until in the sixties, then an influx of federal money turned it into a home for the elderly.  There are some nice looking condo-like apartments there...but it isn't a very good place to play baseball. 

And so the Stars moved to Hamtramack.  By 1931 the depression had brought the Negro National League to an end.  The Stars continued playing as an independent team, and then as part of various short lived leagues.  The team was still alive in 1958 when the owner, Ted Rasberry, decided to rename the team after former negro league star Goose Tatum... Now there is a real nut, but you probably know the Goose better for his antics on the Basketball court. He was the original "Clown Prince" of the Harlem Globetrotters.  Tatum started his career in the 1940s as a baseball player for the Birmingham Black Barons and the Indianapolis Clowns of the (new)Negro National League. It was during this time that he started clowning around on the field to amuse the crowds. Abe Saperstein spotted Tatum clowning around on a baseball field and put him to work.  Not so nutty, he invented the "sky hook" that would make Kareem Jabbar one of the most potent offensive forces in both college and professional basketball. 



The Stars lived only two more years, and the Goose lived seven more after that. 

And this was the day on which the celebration of Lupercalia began in Ancient Rome.  The Holiday derived from the festival of Februa, from which this month gets its name.  It came originally from the Sabine tribes, an ancient tribe from central Italy who were conquered by the Romans around 290 BC. The festival was a fertility ritual in which the women were flogged with an appendage, or organ, of an animal (sorry, I'm not sure what,,,or I'm not bold enough to tell you what) with the supposed result that they would be more likely to bear children. It is through association with this festival that the romantic associations of St. Valentine's Day began, a day that originally had no association with love or relationships. And the theme today is....... yeah, that's nuts.

For the math history freaks, you know who you are.. today is also the birthday of Peter Gustav Dirichlet, the German mathemtician, who was born on Feb 13,1805.  Dirichlet is remembered for a theorem he used in working on Pell's equation, which has more recently become known as the Pigeon-hole theorem.  It seems that term was originate by Paul Erdos in a 1956 paper.  Before that... well here is a note I have from a not-too recent discussion on a history group  by Julio Cabillon. He added that there are a variety of names in different countries for the idea. His list included "le principe des tiroirs de Dirichlet", French for the principle of the drawers of Dirichlet, and the Portugese "principio da casa dos pombos" for the house of pigeons principle and "das gavetas de Dirichlet" for the drawers of Dirichlet. It also is sometimes simply called Dirichlet's principle and most simply of all, the box principle. Jozef Przytycki wrote me to add, "In Polish we use also:"the principle of the drawers of Dirichlet" that is 'Zasada szufladkowa Dirichleta' ". Dirichlet first wrote about it in " Recherches sur les formes quadratiques à coefficients et à indéterminées complexes" (J. reine u. angew. Math. (24 (1842) 291 371) = Math. Werke, (1889 1897), which was reprinted by Chelsea, 1969, vol. I, pp. 533 618. On pp. 579 580, he uses the principle to find good rational approximations. He doesn't give it a name. In later works he called it the "Schubfach Prinzip" [which I am told means "drawer principle" in German]

I had assumed, as stated on the Wolfram "MathWorld" site, that,"This statement has important applications in number theory and was first stated by Dirichlet in 1834". In truth, the principal has been around much longer than Dirichlet, as I found out in June of 2009 when Dave Renfro sent me word that the idea pops up in the unexpected (at least by me) work, "Portraits of the seventeenth century, historic and literary", by Charles Augustin Sainte-Beuve. During his description of Mme. de Longuevillle, who was Ann-Genevieve De Bourbon, and lived from 1619 to 1679 he tells the following story:
"I asked M. Nicole (See below for description of M. Nicole) one day what was the character of Mme. de Longueville's mind; he told me she had a very keen and very delicate mind in knowledge of the character of individuals, but that it was very small, very weak, very limited on matters of science and reasoning, and on all speculative matters in which there was no question of sentiment ' For example,' added he, ' I told her one day that I could bet and prove that there were in Paris at least two inhabitants who had the same number of hairs upon their head, though I could not point out who were those two persons. She said i could not be certain of it until I had counted the hairs of the two persons. Here is my demonstration/ I said to her: M lay it down as a fact that the best-fiimbhed head does not possess more than 200,000 hairs, and the most scantily furnished head b that which has only 1 hair. If, now you suppose that 200,000 heads all have a different number of hairs, they must each have one of the numbers of hairs which are between 1 and 200,000; for if we suppose that there were 2 among these 200,000 who had the same number of hairs, I win my bet But suppose these 200,000 inhabitants all have a different number of hairs, if I bring in a single other inhabitant who has hairs and has no more than 200,000 of them, it necessarily follows that this number of hairs, whatever it be, will be found between 1 and 200,000, and, consequently, be equal in number of hairs to one of the 200,000 heads. Now, as instead of one inhabitant more than 200,000, there are, in all, nearly 800,000 inhabitants in Paris, you see plainly that there must be many heads equal in number of hairs, although I have not counted them.' Mme. de Longuevillle still could not understand that demonstration could be made of the equality in number of hairs, and she always maintained that the only way to prove it was to count them. "
The M. Nicole who demonstrated the principal was Pierre Nicole, (1625 -1695), one of the most distinguished of the French Jansenist writers, sometimes compared more favorably than Pascal for his writings on the moral reasoning of the Port Royal Jansenist. It may be that he had picked up the principal from Antoine Arnauld, another Port Royal Jansenist who was an influential mathematician and logician.

It is the kind of tool you need if you want to prove that there are two people living in Detroit who have exactly the same number of hairs on their head. (honest...no really, that is NOT nuts).

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How Pi almost Was Equal to Three in Indiana

So what about the state that passed a law that set Pi = 3? Well, it was in the paper, and on the internet, but it never happened, although it did get close once. A hoax article was printed and widely circulated (on April 1, 1998) that said that NASA engineers in Huntsville, Alabama were upset about the discovery that the Alabama legislature had just passed a law making Pi=3. When the perpetrators of the hoax realized that the article was being paraphrased (without all the hints that it was a joke, such as the authors name, April Holiday) and circulating as truth, they tried to circulate a notice of the hoax, but found the truth spread much more slowly than the sensational story.
So here is the story of an actual bill (which did NOT pass) that would have set Pi equal to.... well, read on. Notice that in the proposed bill the idea was from a fellow who had already proved many of the impossible constructions of geometry, such as squareing the circle. Here is a another description of the bizarre incident by Cecil Adams from his web column, "Straight Dope":

It happened in Indiana. Although the attempt to legislate pi was ultimately unsuccessful, it did come pretty close. In 1897 Representative T.I. Record of Posen county introduced House Bill #246 in the Indiana House of Representatives. The bill, based on the work of a physician and amateur mathematician named Edward J. Goodwin (Edwin in some accounts), suggests not one but three numbers for pi, among them 3.2, as we shall see. The punishment for unbelievers I have not been able to learn, but I place no credence in the rumor that you had to spend the rest of your natural life in Indiana. [ Although it is often called the Pi Bill, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for the mathematical constant π (pi). In fact pi is not mentioned in the text of the bill.]

The text of the bill consists of a series of mathematical claims followed by a recitation of Goodwin's previous accomplishments:

"... his solutions of the trisection of the angle, doubling the cube and quadrature of the circle having been already accepted as contributions to science by the American Mathematical Monthly ... And be it remembered that these noted problems had been long since given up by scientific bodies as unsolvable mysteries and above man's ability to comprehend."

Goodwin's "solutions" were indeed published in the AMM, though with a disclaimer of 'published by request of the author'.

If you feel up to the task, the bill can be found here.

Just as people today have a hard time accepting the idea that the speed of light is the speed limit of the universe, Goodwin and Record apparently couldn't handle the fact that pi was not a rational number. "Since the rule in present use [presumably pi equals 3.14159...] fails to work ..., it should be discarded as wholly wanting and misleading in the practical applications," the bill declared. Instead, mathematically inclined Hoosiers could take their pick among the following formulae:
(1) The ratio of the diameter of a circle to its circumference is 5/4 to 4. In other words, pi equals 16/5 or 3.2
(2) The area of a circle equals the area of a square whose side is 1/4 the circumference of the circle. Working this out algebraically, we see that pi must be equal to 4.
(3) The ratio of the length of a 90 degree arc to the length of a segment connecting the arc's two endpoints is 8 to 7. This gives us pi equal to the square root of 2 x 16/7, or about 3.23.

There may have been other values for pi as well; the bill was so confusingly written that it's impossible to tell exactly what Goodwin was getting at. Mathematician David Singmaster says he found six different values in the bill, plus three more in Goodwin's other writings and comments, for a total of nine.

Lord knows how all this was supposedly to clarify pi or anything else, but as we shall see, they do things a little differently in Indiana. Bill #246 was initially sent to the Committee on Swamp Lands. The committee deliberated gravely on the question, decided it was not the appropriate body to consider such a measure and turned it over to the Committee on Education. The latter committee gave the bill a "pass" recommendation and sent it on to the full House, which approved it unanimously, 67 to 0.

In the state Senate, the bill was referred to the Committee on Temperance. (One begins to suspect it was silly season in the Indiana legislature at the time.) It passed first reading, but that's as far as it got. According to The Penguin Dictionary of Curious and Interesting Numbers, the bill "was held up before a second reading due to the intervention of C.A. Waldo, a professor of mathematics [at Purdue] who happened to be passing through." Waldo, describing the experience later, wrote, "A member [of the legislature] then showed the writer [i.e., Waldo] a copy of the bill just passed and asked him if he would like an introduction to the learned doctor, its author. He declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know."

The bill was postponed indefinitely and died a quiet death. According to a local newspaper, however, "Although the bill was not acted on favorably no one who spoke against it intimated that there was anything wrong with the theories it advances. All of the Senators who spoke on the bill admitted that they were ignorant of the merits of the proposition. It was simply regarded as not being a subject for legislation."

Tennessee is also frequently mentioned as a state that "passed a pi=3 bill" but that seems to come from a small reference by Robert Heinlein in Stranger in a Strange Land. "In the Tennessee legislature a bill was again introduced to make the ratio pi exactly equal to three"."

* Much of the text was taken from http://www.straightdope.com. and Wikipedia

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