Let ε < 0.


State of the union

Filed under: Puns, Seasons greetings — Travis @

In deference to this week’s historic inauguration, I’ve decided to present a mathematician’s take on Shepard Fairley’s iconic red-blue-and-blue CHANGE and HOPE Obama posters.


Deck the board with differentials

Filed under: Harmonic analysis, Seasons greetings — Travis @

–by Dennis Gannon (1940-1991)
(Sung to the tune of Deck the Halls)

Fill the boards with differentials,
Fa-la-la-la-la La-la-la-la.
Note that du’s are essential,
Fa-la-la-la-la La-la-la-la.
C’s are constants here before us,
Fa-la-la La-la-la La-la-la.
Integration cannot floor us,
Fa-la-la La-la-la La-la-la.

Quizzes always make us queasy,
Fa-la-la-la-la La-la-la-la.
Max and mins are never easy,
Fa-la-la-la-la La-la-la-la.
Conic volumes we can measure,
Fa-la-la La-la-la La-la-la.
The FTC we’ll always treasure,
Fa-la-la La-la-la La-la-la.

You can find another Dennis Gannon Calculus Carol here.


The riddle of the elves

Filed under: Seasons greetings — Travis @

Old Santa’s pack held 30 toys
Made by his elfin crew;
And though none made the same amount,
Each elf made more than two.
The elf named Joy made one more toy
Than the elf who dressed in red;
But Joy made one less Christmas toy
Than the elf who made each sled.
Spry Johnny Elf made racing cars;
Five toys were made by Jane.
The elf who dressed in yellow suits,
Made each and every train.
The elf who always dressed in green,
Made one-third as many as Sue.
Cute Marcia Elf was dressed in orange,
And one elf dressed in blue.
The elf who made the spinning tops,
Made the most toys of them all.
Another perky smiling elf
Made each and every ball.
From the clues can you yourselves
Work out the puzzle of the elves?


Christmas riddles

Filed under: Riddles, Seasons greetings — Travis @

How does a mathematician wish you a merry Christmas?
A: Like this:

Q: How does an engineer wish you a merry Christmas?
A: Like this:

(Click to enlarge.)

Q: Why do computer scientists confuse Christmas and Halloween?
A: Because Oct 31 = Dec 25.


O calculus, O calculus!

Filed under: Harmonic analysis, Seasons greetings — Travis @

– by Dennis Gannon (1940-1991)
(Sung to the tune of O Tanunbaum)

Oh calculus; oh calculus!
How tough are both thy branches.
O calculus; O calculus!
To pass, what are my chances?
Derivatives I cannot take,
At integrals my fingers shake.
O calculus; O calculus!
How tough are both thy branches.

O calculus; O calculus!
Thy theorems I can’t master.
O calculus; O calculus!
My proofs are a disaster.
You pull a trick out of the air,
Or find a reason God knows where.
O calculus; O calculus!
Thy theorems I can’t master.

O calculus; O calculus!
Thy problems so distress me.
O calculus; O calculus!
Related rates depress me.
I walk toward lampposts in my sleep,
And running water makes me weep.
O calculus; O calculus!
Thy problems so distress me.

O calculus; O calculus!
My limit I am reaching.
O calculus; O calculus!
For mercy I’m beseeching.
My grades to not approach a B,
They’re just an epsilon from D.
O calculus; O calculus!
My limit I am reaching.

Dennis Gannon was the head of the society for Isaac Newton and an inspiring teacher at F. T. Maloney High School in Meriden, CT for 29 years. Each year at the holiday season he bellowed out Calculus Carols that he wrote for his AP students. This is one of them.


Santa Claus: an engineer’s perspective

Filed under: Science humor, Seasons greetings — Travis @

I. There are approximately two billion children (persons under 18) in the world. However, since Santa does not visit children of Muslim, Hindu, Jewish or Buddhist religions, this reduces the workload for Christmas night to 15% of the total, or 378 million (according to the Population Reference Bureau). At an average (census) rate of 3.5 children per house hold, that comes to 108 million homes, presuming that there is at least one good child in each.

II. Santa has about 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west (which seems logical). This works out to 967.7 visits per second. This is to say that for each Christian household with a good child, Santa has around 1/1000th of a second to park the sleigh, hop out, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left for him, get back up the chimney, jump into the sleigh and get on to the next house.

Assuming that each of these 108 million stops is evenly distributed around the earth (which, of course, we know to be false, but will accept for the purposes of our calculations), we are now talking about 0.78 miles per household; a total trip of 75.5 million miles, not counting bathroom stops or breaks. This means Santa’s sleigh is moving at 650 miles per second — 3,000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle, the Ulysses space probe, moves at a poky 27.4 miles per second, and a conventional reindeer can run (at best) 15 miles per hour.

III. The payload of the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium sized Lego set (two pounds), the sleigh is carrying over 500 thousand tons, not counting Santa himself. On land, a conventional reindeer can pull no more than 300 pounds. Even granting that the “flying” reindeer could pull ten times the normal amount, the job can’t be done with eight or even nine of them Santa would need 360,000 of them. This increases the payload, not counting the weight of the sleigh, another 54,000 tons, or roughly seven times the weight of the Queen Elizabeth (the ship, not the monarch).

IV. 600,000 tons traveling at 650 miles per second creates enormous air resistance — this would heat up the reindeer in the same fashion as a spacecraft re-entering the earth’s atmosphere. The lead pair of reindeer would absorb 14.3 quintillion joules of energy per second each. In short, they would burst into flames almost instantaneously, exposing the reindeer behind them and creating deafening sonic booms in their wake. The entire reindeer team would be vaporized within 4.26 thousandths of a second, or right about the time Santa reached the fifth house on his trip. Not that it matters, however, since Santa, as a result of accelerating from a dead stop to 650 m.p.s.. in .001 seconds, would be subjected to centrifugal forces of 17,500 g’s. A 250 pound Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by 4,315,015 pounds of force, instantly crushing his bones and organs and reducing him to a quivering blob of pink goo.

V. Therefore, if Santa did exist, he’s dead now.

Merry Christmas.

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