Seriously

No getting 'round it: today is π day.

Make mine pecan.  (Aren't all mathematicians a little bit nuts?)

The printer dropped his tray.  Everything was pied.

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Pi Day

Today is National Pi Day,  3.14, get it?

Coincidentally it is also the anniversary of the birth of probably the most famous theoretical physicist of his time.  Albert Einstein 14 March 1879 – 18 April 1955



To celebrate Pi Day, please have a nice slice of pie, fruit pie of course, and certainly the pie should be round.

Grace from Dragon's Alley sent us this sweet little pie song by:
Quincey Coleman

Margot and the Pink Elephant #T

It is a well-known mathematical fact that there are three and only three regular tessellations of the plane..  I offer no proof for this, but it is a fact.

I was thinking a few years ago about the ways in which tessellation of the plane might be accomplished with other sorts of figures.  I designed this little example, which would look really neat if the elephants were pink, and you might just wonder. . .

Margot's sixth birthday coincided with the arrival of the circus in town so of course her Mama took her to see the parade touting the coming performances.  As they stood along the curb watching the passing wagons and lumbering beasts, Margot was dancing with excitement, pointing, exclaiming, and oohing and aahing.

But as the elephants approached, Margot suddenly got very quiet and very still.  Very un-Margot-like behavior indeed.  The first behemoth was pink.  All over pink.  Mother could see that the attendant for whatever reason had dusted the animal all over with pink powder of some sort.  But little Margot's comprehension was addled, or as we would say in this day and age, her mind was blown.

Margot's shriek and a mighty shriek it was coming as it did from such a small body could have been heard in the next county.  At any rate, the elephants heard it and immediately the vast pink elephant responded with a clarion trumpet call that could have been heard two counties over. This was instantly followed by an elephant sextet that virtually deafened everyone in town and the applause of the lions and tigers as they roared from their cages increased the cacophony to a level never before nor ever since heard in that town. The dappled mare reared, the bareback rider rolled in the street, her tutu and tights mangled and dirty, and so were her knees and elbows.

Then the zebras broke out of their wagon. . .

Margot is up in years now, and to this day she excuses herself and leaves the room whenever someone mentions "the day the circus came to town."

© 2015 David W. Lacy

*For really cool tessellations study M. C. Escher

M. C. Escher

John Nash, Mathematician

Reading about the recent death of John F. Nash and his wife Alicia led to numerous revelations for me.  Yes, I saw "A Beautiful Mind."  I spent the following days of discussion with my spouse attempting to explain to her what we saw.  Blind leading the blind?  Perhaps.

John Nash who would want to be remembered as a mathematician will in all likelihood be as much if not more remembered as an economist.  It was in the field of economics in which he won the Nobel Prize.  Economists in large measure believe Nash's contributions to the field are at the minimum as important as were those of Adam Smith.

Everyone who has read the book A Beautiful Mind or who saw the cinematic production knows that Nash was brilliant almost beyond the comprehension of most people and moreover they know that he was a life-long sufferer of schizophrenia.  I shall make no attempt to detail his battle  It is to be noted that he and his wife left behind a son John, Jr. who holds a Ph.D. in his own right and who also suffers from schizophrenia.  It was one of his mother's major worries: What will become of Johnny when we are gone?

But one of the more sobering statistics I garnered in my reading was this.  Twenty-five percent of all Americans suffer from some form of mental illness.

The next time you are in a room with three other people look around.

In addition to John, Jr., Dr. Nash is also survived by another son, John Stier.

John Forbes Nash, Jr.  1928 - 2015
Alicia Lopez-Harrison Nash 1933 - 2015
RIP

Fork in the Road: Two

High school graduation ceremonies were held in Civic Center auditorium on June 11.  About five days later I received a telephone call from a local accounting firm.  They tendered a flat-out job offer.  I had not sought such a position.  I was stunned.  "Why me?'  "We talked to your senior math teacher and explained to him that we wanted a talented math student, one willing to learn our system and who was not necessarily college material.  We don't want a college graduate.  We will teach you our methods, and you will be an earning member of society.  You can start tomorrow!"

I told the caller I would need to think about it.  I would let him know.  I was told not to take too long. They would hold the position open for me until Friday.  Now how does one react to that?

 Y.  Left fork, or right?

What a flattering offer.  The money from the start was more than I had ever dreamed I could earn.  Old Mr. B had such confidence in my ability, and the company such confidence in Mr. B's integrity, that it was a sealed deal before I even knew there was a deal.

I started immediately.  I spent day after unending day putting little numerals in little squares.  Number three pencils and thin-line pens became my stock in trade.  Mathematics is exciting, which is why Mr. B perceived me as an enthusiastic learner.  Little numerals in little squares are not exciting.  In fact, the level of boredom accelerated faster than my ability to spend the money I was taking home.

I started "clubbing."  Yes, I was too young to enter a bar, but there were places.  I found them.  I started fooling with women  I could never take home to mother.  The drinking soon accelerated from weekend nights to a bottle on the nightstand and a snort now and then, then...

Soon I was no longer able to see the little numerals well enough to place them in the little boxes.  In less than six years, that is to say before I was twenty-four years of age, my emotional health was a wreck, my physical health was well on the way to total disrepair, and I was unemployed.

Actually, my first thought was, Thanks, Mr. B, and since you think I'm not college material, I've just decided I will go to college, so there!  Then I called the company and advised them that I was not interested in the offer.

My little fantasy journey down the "wrong" fork is fraught with several difficulties, but it is fantasy.  I would truly be bored to tears in such a job, but the wine, women, and song is a highly unlikely outcome even in the face of such ennui.  I have an addictive personality, hence I stay away from known addictants (spell check says that's not a word;  I respectfully disagree).

I have always believed that I chose the "right" fork in that road, notwithstanding Mr. B was a bit put off by my cavalier response to his attempt to help me along life's highway.

Gift Scarf and Möbius

My sister, Ilene, gave to BBBH an "Infinity Scarf."  Trade-name, I guess.  Anyway, one glance at the beautifully-made fabric item assured me that it was a Möbius strip.  I announced this information to the gift recipient at once.  She was less than interested.

So I started with my standard seventh-grade presentation of the concept.  A  Möbius strip is a geometric figure which has only one side, and possesses but one edge.  (She:  So?)  Clearly this was going to rival in difficulty the actual presentation to a seventh grade class.

It is lots of fun to make a paper model of this figure with its weird properties, for with a pencil and a pair of scissors some amazing results can be obtained. (So?)

I am now talking to myself.  I did not even get to the rudimentary math involved, and that is the real fun!  The advantage lies with the seventh graders, for they are a captive audience, and may not wander from the precinct at will.

Never mind the background.

The Integers

Leopold Kronecker (December 7, 1823 – December 29, 1891) was a German mathematician who famously said, "God made the integers; all else is the work of man."

There are, I suppose, many ways in which to interpret this statement. I do not presume to know what Kronecker's intent was, though I rather hope he intended to confine man's "creation" in this instance to the world of mathematics. In such case, he may have been right. If the intent was to state that except for the integers, all creation was accomplished by man, Image: Wikipedia then that is ludicrous.


It is a matter of record that on this statement hinged the alienation of Kronecker from his more famous student, Georg Cantor, who was not buying the statement in any of its possible permutations. Or at least, so say some math historians. It is certainly the case that the two gentlemen represented opposing philosophies of mathematics.

Arithmetic reminder: Take your clock and Spring Forward one hour before you fall asleep!