MATHEMATICAL BELATED HOLIDAY GREETING

Given                                                                          2 m r [i cos r² – sin r²] = dx/dr

Separate variables                                                      2 m r dr [i cos r² – sin r²] = dx

Divide both sides by m                                                2 r dr [i cos r² – sin r²] = dx/m

Express each side as an integral                                 ∫ 2 r dr [i cos r² – sin r²] = ∫ dx/m

Integrate                                                                     cos r² + i sin r² + c₁ = x/m + c₂

Subtract c₂  from both sides                                        cos r² + i sin r² + c₁ – c₂= x/m

c₁ – c₂ = c² for some c                                                 cos r² + i sin r² + c² = x/m

Multiply both sides by m                                             m [cos r² + i sin r²] + m c²= x

E = m c²                                                                       m [cos r² + i sin r²] + E = x

Subtract E from both sides                                         m [cos r² + i sin r²] = x – E

De Moivre’s rule:  exp (ø i) = cos ø + i sin ø               m exp (r² i) = x – E

E (work) = force . distance                                         m exp (r² i) = x – F.s

F (force) = mass times acceleration                           m exp (r² i) = x – mas

r² = rr                                                                           m exp (rri) = x – mas

exp (a) = e^a                                                                  m e^rri = x – mas

(Apparently originated with Brett Stevens, “Seasonal Greeting,” in the New Scientist, 21-28 December 1991)

PREDICTION

TOM GILL PREDICTS:  If Jim Harbaugh is fired by the San Francisco 49ers after the end of the 2014 regular season, and a new coach is not immediately named, look for Adam Gase (currently offensive coordinator for the Denver Broncos) to get the job- at least be officially interviewed.

THE LAWYER AND THE SENIOR CITIZEN

(Note: There are many versions of this, involving "a lawyer and a Blonde," "a hardware engineer and a software engineer," "an American and a Nigerian," "a white man and a Native American," "a medical doctor and an engineer," "a Russian and a Ukranian," "an Indian and a Pakistani," "an Italian and an Irishman," "a Yankee fan and a Red Sox fan," etc.)

A lawyer and a senior citizen are sitting next to each other on a long flight.   The lawyer is thinking that seniors are so dumb that he could get one over on them easily.   So, the lawyer asks if the senior would like to play a fun game.   The senior is tired and just wants to take a nap, so he politely declines and tries to catch a few winks.   The lawyer persists, saying that the game is a lot of fun ... "I ask you a question, and if you don't know the answer, you pay me only $5.00. Then, you ask me one, and if I don't know the answer, I will pay you $500.00," he says.   This catches the senior's attention and, to keep the lawyer quiet, he agrees to play the game with him.   The lawyer asks the first question. "What's the distance from the Earth to the Moon?"   The senior doesn't say a word, but reaches into his pocket, pulls out a five-dollar bill, and hands it to the lawyer.   Now, it's the senior's turn. He asks the lawyer, "What goes up a hill with three legs, and comes down with four?"   The lawyer uses his laptop to search all references  and, he can't find anything on the InterNet. He sends E-mails to all the smart  friends he knows; and all to no avail. After an hour of searching, he finally gives up.   He wakes the senior and hands him $500.00. The senior pockets the $500.00 and goes right back to sleep.   The lawyer is going nuts now, not knowing the answer. He wakes the senior up again and asks, "Well, so what goes up a hill with three legs and comes down with four??"   The senior reaches into his pocket, hands the lawyer $5.00, and goes back to sleep.