Saki starting new job as mathematician, September 1995



Mathematics Page

Last updated October 11, 2014



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The above photo was taken of me in September 1995, when I started my first job out of college as a mathematician.


Two engineers decided to rent a hot air balloon and tour the countryside.  Their balloon got too high and they got caught in a strong wind that sent them several miles off course.  Eventually, they got their balloon closer to the ground.  They saw a man walking around by himself and they yelled to him, "Hey, where are we!"  The man looked up at the balloon, looked down at his shoes, scratched his head, looked back at the balloon, looked down at his shoes, then yelled back, "You're in a hot air balloon!"  The more senior engineer looked to the junior engineer and said, "That fellow is obviously a mathematician."  "How do you know that?" inquired the junior engineer.  The senior engineer replied, "Because he had to think about the question a long time, he was absolutely correct, and his answer did us absolutely no good whatsoever."

A mathematician, a biologist, and a physicist were sitting outside their house one day which sat directly across the street from a vacant house.  They then saw a couple enter the house.  After about an hour, they saw three people leave.  They found that to be most peculiar and pondered over what might have happened.  The biologist said they obviously reproduced, hence producing the third person.  The physicist said their data was clearly incorrect and they must have counted incorrectly.  The mathematician thought about it, looked down at his shoes, scratched his head, and replied, "Whatever the case, if one more person goes back into the house, it will be empty again."

How do you tell the difference between an extroverted and an introverted mathematician?
The extroverted mathematician looks at YOUR shoes.

A mathematician is a machine that transforms caffeine into theorems.

Math and alcohol don't mix. Don't drink and derive.

A mathematician was walking through the woods one day and he heard a beautiful voice, "Greetings kind sir."  He looked around and saw nothing.  When he glanced back down at his shoes he saw a frog.  The frog said, "I'm not really a frog.  I'm actually a beautiful young princess.  An evil witch cast a spell upon me to change me into a frog but if you kiss me, I'll change back into a beautiful princess and I will make mad, passionate love to you."  The mathematician looked around, looked down at the frog, looked at his shoes, then picked up the frog, threw it in his bag, and walked off with it.  The frog yelled out from the bag, "Hey!  Didn't you hear me?  I said if you kiss me, I'll turn into a beautiful princess and make mad, passionate love to you!"  The mathematician yelled to the frog, "I'm a mathematician.  I don't care about girls or sex.  But a talking frog I can use."

A ham sandwich is better than all the happiness in the world. Don't believe me? Here's the proof.
Nothing is better than all the happiness in the world.
A ham sandwich is better than nothing.
Hence, by transitivity, a ham sandwich is better than all the happiness in the world.
From Professor Scott Farrand, 1994, California State University Sacramento (CSUS).

A physicist, an engineer, and a statistician are at the shooting range one day. There is only enough money for one target so they decide to share. The physicist calculates the range to the target and makes the proper elevation adjustment. He gently squeezes the trigger and sends a round downrange, missing the center of the target with his round striking 4 inches too far to the left. The engineer uses the data the physicist calculated but also accounts for wind. He fires off a round, also missing the center of the target with his round striking 4 inches too far to the right. Upon seeing this, the statistician yells, "Bullseye!"

One day, a liberal arts student, a statistician, and a mathematician were in a car, driving through Ireland. They passed a cow with pink stripes. The liberal arts student commented, "Interesting, cows in Ireland have pink stripes." The statistician quickly interupted saying, "You liberal arts types make a single observation then draw a conclusion about the entire population. The only correct statement you can make based on a single sample is that the one cow you saw has pink stripes." The mathematician then interjected, "Actually, the only correct conclusion is that the cow we saw has pink stripes on one side."
     Cow saying mu

A father who was raised out in a remote part of the country never had the chance to get an education past the 5th grade. He worked hard all his life and was a little skeptical of sending his son to school. But to abide with the state laws, he sent his son to school. The son came home and the father asked the son, "Boy, what be you learn in school today?"
The son replied, "I learnt me some geometry."
The father said, "What you learnin' in geometry?"
The son said, "Pi R squared."
The father replied, "Boy, them city folk teachin' you all wrong! It ain't pi R squared! Pie are round, cornbread are square."

A REAL square root.
Proof that God is a mathematician and has a sense of humor.
From Nicole Leahy.
     A real square root

Smart man + smart woman = romance
Smart man + dumb woman = affair
Dumb man + smart woman = marriage
Dumb man + dumb woman = pregnancy

Smart boss (Lynn) + smart employee (me) = profit
Smart boss + dumb employee = production
Dumb boss + smart employee = promotion
Dumb boss + dumb employee = overtime

A man will pay $2 for a $1 item he needs.
A woman will pay $1 for a $2 item that she doesn't need.

A woman worries about the future until she gets a husband.
A man never worries about the future until he gets a wife.
A successful man is one who makes more money than his wife can spend.
A successful woman is one who can find such a man.

Proof that Girls are Evil
It is a known fact that girls require both time and money. Thus,

girls = time x money

It is also a known fact that time is money.

time = money

Therefore, by substitution,

girls = time x money = money x money = money^2

But money is the root of all evil

money = sqrt(evil)

Again, by substitution,

girls = money^2 = (sqrt(evil))^2 = evil

Hence, girls are evil

girls = evil

3.39 Dollars for a Quart?
one quart = 32 ounces
16 ounces = one pound
0.59 pounds = one dollar (as of June 19, 2003)
one quart = 3.39 dollars

Getting a Phd (not that I have one) means reading two papers that have never been read to write a paper that never will be read.

If my eyes are closed, I'm conducting research.  If my eyes are closed and I'm snoring, I'm conducting advanced research.

Son of a bitch
A little boy was doing his math homework. He said to himself, "Two plus five, that son of a bitch is seven. Three plus six, that son of a bitch is nine."

His mother heard what he was saying and gasped, "What are you doing?"

The little boy answered, "I'm doing my math homework, Mom."

"And this is how your teacher taught you to do it?" the mother asked.

"Yes," he answered.

Infuriated, the mother asked the teacher the next day, "What are you teaching my son in math?"

The teacher replied, "Right now, we are learning addition."

The mother asked, "And are you teaching them to say two plus two, that sone of a bitch is four?!"

After the teacher stopped laughing, she answered, "What I taught them was two plus two, the sum of which is four."
- from the Nisei Post 8985 Veterans of Foreign Wars (VFW) Newsletter, Volume 25, Number 10, April 2006

A Man Who Knows His Math
I was riding to work yesterday when I observed a female driver, who cut right in front of a pickup truck, causing the driver to drive onto the shoulder to avoid hitting her.

This evidently angered the driver enough that he hung his arm out his window and gave the woman the finger.

'Man, that guy is stupid,' I thought to myself. I ALWAYS smile nicely and wave in a sheepish manner whenever a female does anything to me in traffic, and here's why:

I drive 48 miles each way every day to work.

That's 96 miles each day.

Of these, 16 miles each way is bumper-to-bumper.

Most of the bumper-to-bumper is on an 8 lane highway.

There are 7 cars every 40 feet for 32 miles.

That works out to 982 cars every mile, or 31,424 cars.

Even though the rest of the 32 miles is not bumper-to-bumper, I figure I pass at least another 4000 cars.

That brings the number to something like 36,000 cars that I pass every day.

Statistically, females drive half of these.

That's 18,000 women drivers!

In any given group of females, 1 in 28 has PMS.

That's 642.

According to Cosmopolitan, 70% describe their love life as dissatisfying or unrewarding.

That's 449.

According to the National Institute of Health, 22% of all females have seriously considered suicide or homicide.

That's 98.

And 34% describe men as their biggest problem.

That's 33.

According to the National Rifle Association, 5% of all females carry weapons and this number is increasing especially in California.

That means that EVERY SINGLE DAY, I drive past at least one female that has a lousy love life, thinks men are her biggest problem, has seriously considered suicide or homicide, has PMS, and is armed.

Give her the finger?

I don't think so.

Math and sex...two of my favorite things, but not necessarily in that order.

Real mathematicians say that math isn't about is about relationships.

How to write like a mathematician
1. Use the royal "we." For example, instead of writing "I begin by defining the random variable X" write "We begin by defining the random variable X." It doesn't matter if it is only you who are writing the paper. Mathematicians are a bit schizophrenic.
2. Define the obvious.
3. Fail to define that which needs clarifying.
4. Use complex terms to state that which can be stated simply.
5. Use undescriptive variable names.
6. Assume the reader has technical skills which he or she probably does not.
7. Leave out concrete examples. Abstract examples are fine.
8. Make sure a large proportion of your sentences begin with the words "hence," "therefore," and "thus." Some sentences should contain the phrases "without loss of generality" or "clearly it is obvious."
9. Ensure your font is small enough so that once your paper is copied, the subscripts and superscripts will be unreadable.
10. The title of your paper should be sound sophisticated, the abstract should be confusing, and the only people who should fully understand the body of the paper in its entirety are the author and people with graduate degrees in same the area of expertise as the author.
11. A few Greek letters should be used just to prove your level of competence with Latek.

If someone sends you a simple, well stated, fully self contained question (e.g. "What is the Unix command to determine the number of characters in a text file?") your first reply should be "What is it you are trying to do?" Then, instead of answering the question, reply with a series of other questions. Never admit that you don't know the answer. Instead, just make alternative suggestions. Make sure these alternatives are never simple. Continue this process of asking questions and suggesting complex alternatives until the person who asked the original question
1. doesn't realize or simply forgets that you just don't know the freaking answer.
2. thinks you are a genius.
3. never bothers you again with questions.

Professor Griffin's Gambling Algorithm
Let's say you are playing a game where the chance of winning is 4 in 10.  If you lose, you get nothing.  If you win, you get back what you bet plus an equal amount.  Thus, for every dollar you bet, you "expect" to get back 0.80.  This is similar to the formula for calculating the average: probability of winning times the amount you receive when you win, or (4/10) x 2.  Based on this game, let's say your goal is to leave with $10.  In order to accomplish this in a single play, you need to bet $5.  So this is how much you bet.  Stop if you win.  If you lose, then you need to win $15 in order to win the $10 plus the $5 you lost on the first play.  To meet this $15 goal, you bet 7.50 on the second play.  Stop if you win.  If you lose, then you need to win $22.50 to win the $10 plus the $5 + $7.50 = $12.50 you lost on the first and second plays.  So you bet $11.25.  Continue this pattern.  Thus, we bet in the following manner:

Play #

Need to win

Bet to place

Probability of losing plays 1 through n

































Note that this is true only if we assume that the probability of a win in 0.4.  This formula is easily adjusted if this is not the case and the probability of a win is known value.  We see that any win accomplishes our mission which is to walk away with 5 more than we started.  Thus, we quit as soon as we win.  The problem with this algorithm is that it could require a good deal of money to be relatively certain of winning a moderate amount.  We see that the probability of losing all 4 plays is 0.1296 and the amount of money needed to bet on the 4th play is 16.875.  This means we would need a total of 40.625 to make it this far.  To be very confident of a win, we might want to be prepared for up to 9 plays, thus ensuring that the probability of all 9 losses is (0.6)^9=0.010077696 or about 1%.  But this would require a rather large amount of money to be placed on the last bet and a VERY large amount of total money to ensure we can place bets 1 through 8.  Hence, while this algorithm almost guarantees a win, it also requires a relatively large amount of money to be certain of a moderately sized prize.  Like most any investment, large rewards are almost always accompanied by large risks.

This was taught to me by the late Professor Peter A. Griffin, USMC rifleman and author of "The Theory of Blackjack." Not the dude from Family Guy (the cartoon).

Burnt pancake problem
There are certain math problems that I really love. The following is one such example. The question is worded simply, in a way that anyone can understand. The answer can be obtained mathematically or through logic. I've been told that mathematicians and lawyers are good at solving such probems.

Say I'm making pancakes. The first one is burned on both sides. The second one is better-only one side burned. The third one is okay on both sides. I choose a pancake at random and observe that one side is not burned. What are the chances the other side isn't burned, either?

If you said one out of two, then you are thinking of individual pancakes (of which there are two) rather than the unburnt sides (of which there are three).

The correct answer is two out of three.

Here's the explanation.

This is what you are given.

Pancake 1

Pancake 2

Pancake 3

Side A



Not burnt

Side B


Not burnt

Not burnt

Clearly, pancake one doesn't matter. That's right it's as if if N'sync and the Backstreet Boys traded guys. It doesn't matter.

The only things that matter are the unburnt sides. So let's consider our possibilities.

Pancake 2, side B

The other side is burnt

Pancake 3, side A

The other side is not burnt

Pancake 3, side B

The other side is not burnt

Hence, there are 3 possibilities, of which, 2 give us unburnt opposite sides.

- from Parade - Ask Marilyn - Can You Answer This Interview Question?

Monty Hall Problem
This is one of my favorite problems. It is based on a game show called "Let's Make a Deal" that I sometimes watched as a child. Monty Hall was the host.

Suppose you're on a game show, and you're given the choice of three doors.

Behind one door is a car; behind the others, goats. You pick a door...say number one, and the host, who knows what's behind the doors, opens another door, say number three, which has a goat. He then says to you, "Do you want to pick door number two?" Is it to your advantage to switch your choice?

The answer is yes. Most people will say no, believing that your chances remain the same. But the fact that the host has knowledge of what is behind the doors make all the difference.

Rather than try to elaborate on this logic, I'll simply exhaust over all cases, assuming door one is chosen.

These are the possibilities:

Behind door 1

Behind door 2

Behind door 3

Case A




Case B




Case C




Now we'll consider the possible outcomes if you stick with your choice of door 1.

Behind door 1

Behind door 2

Behind door 3

Result if sticking with door 1

Case A





Case B





Case C





Clearly, you chances of winning a car if sticking with door number one is 1 in 3.

Let's see what happens if you take Monty up on his offer and switch doors.

Behind door 1

Behind door 2

Behind door 3

Result if switching to the door offered

Case A





Case B





Case C





Based on the above, if you switch to the door offered, then your chances of winning the car become 2 in 3.

The cases for if you initially pick door number two or three follow the same logic...that is, you're better off switching to the door offered rather than sticking with your first choice.

- from Wikipedia - Monty Hall Problem

What Kind of Animal is This?
[The limit as x->infinity of (1+1/x)^x] [The summation over all i of pr(i)*i]

Bridge Over Troubled Waters

Four men from the Howard County Striders were out running one day.  They were out training for a marathon, having run a good 15 miles when it started getting dark.  Fortunately, one of them had a flashlight.  They weren't exactly sure where they were but shortly after the sun set, they came to a familiar landmark, an old bridge.  This bridge was very weak and couldn't hold more than 2 people at a time.  When anyone was on the bridge, they had to have the flashlight, either with them, or with the other runner right next to them.  The bridge stood high above a roaring river.  The runners couldn't get across the river at any other point, and if they turned back, they risked getting lost again.  Their only option was to continue on.

  • Mick could cross the bridge in 1 minute
  • Nikki could cross it in 2 minutes
  • Tommy could cross it in 5 minutes
  • Vince could cross it in 10 minutes (he was injured)

What is the shortest amount of time to get all 4 runners on the other side of the bridge?

For example, if we want to get Nikki and Tommy across the bridge, one must hold the flashlight and they can only move as fast as the slower runner, Tommy.  Then they somehow need to get the flashlight back to the other runners so Nikki might take it back.  That would take a total of 5 + 2 = 7 minutes.

Lineman's Problem

Pole A of height a, perpendicular to the ground.
Pole B of height b, perpendicular to the ground.
The distance between A and B is c.

What is the shortest length of wire required to connect the top of A to the top of B in such a way that the wire must also touch the ground?

Save the calculus for your dentist

What is a trilobite made of?

Number of the Beast

The Beauty of Math
Here's something my Aunt Kay forwarded to me.

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Brilliant, isn't it?

And look at this symmetry:

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321

What Equals 100%? What does it mean to give MORE than 100%? Ever wonder about those people who say they are giving more than 100%? We have all been in situations where someone wants you to GIVE OVER 100%. How about ACHIEVING 101%?

What equals 100% in life?

Here's a little mathematical formula that might help answer these questions:

     A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
is represented as
     1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
     8+1+18+4+23+15+18+11 = 98%
     11+14+15+23+12+5+4+7+5 = 96%
     1+20+20+9+20+21+4+5 = 100%

THEN, look how far the love of God will take you
     12+15+22+5+15+6+7+15+4 = 101%

Therefore, one can conclude with mathematical certainty that while Hard Work and Knowledge will get you close, and Attitude will get you there, it's the Love of God that will put you over the top!

Golden Tit
A golden rectangle is a rectangle with dimensions which are of the golden ratio. The golden ratio is approximately 1.618033988749894848204586834366 to one. It is exactly (sqrt(5)+1)/2:1. To construct a golden rectangle:
     1. Draw a square.
     2. Measure the distance of the diagonal of the square.
     3. Use the length of this diagonal to extend one of the sides of the square.
     4. Use the endpoint of the extended side to create a rectangle.
Golden rectangles are found frequently in art and architecture because its shape is said to be aesthetically pleasing to the eye.
Golden rectangle construction

Though tastes in breast shape differ greatly, there is no denying that certain shapes tend to be more appealing than others. It is my opinion that the golden rectangle is also one that defines the perfectly shaped woman's breast. I wonder if Howard Stern would agree?
Golden rectangle construction


What kind of animal is this?

[The limit as x->infinity of (1+1/x)^x] [The summation over all i of pr(i)*i]

It's an emu.  The first part is


while the second part is mu, as in the arithmetic mean.

Answer to bridge over troubled waters question
Mick (1) and Nikki (2) run across the bridge with the flashlight.  2 minutes
Mick (1) runs back with the flashlight.  1 + 2 = 3 minutes
Tommy (5) and Vince (10) run across the bridge with the flashlight.  10 + 1 + 2 = 13 minutes
Nikki (2) runs back across the bridge with the flashlight.  2 + 10 + 1 + 2 = 15 minutes
Mick (1) and Nikki (2) run across the bridge with the flashlight.  2 + 2 + 10 + 1 + 2 = 17 minutes

Hence, the answer is 17 minutes.

Answers to Lineman Problem
Imagine reflecting B through the ground. Call this reflection B'.  String a wire from the top of A to the bottom of B'.  Call the point at which the wire touches the ground point D.  Let D also be the point where the wire touches when connecting from the top of A to the ground, then the ground to the top of B.  Note that the length of wire required to accomplish this is the same as the length required to connect the top of A to the bottom of B'.  The length of wire that connects these points, m, is minimal because the shortest distance between two points is a straight line.  Hence, using Pythagorean's Theorem, the answer is m = sqrt((a+b)^2 + c^2).

Real mathematicians don't do arithmentic

Answer to trilobite question
A trilobite is made of eight trilobits.


Ask Doctor Math

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The Oddball Problem
This is one of those great problems where the question is worded very simply and the solution seems like it should be simple but believe you me, it isn't.

University of Maryland College Park (UMCP)
Directions: From where highway 695 (Baltimore beltway) meets highway 95, take highway 95 south for about 19 miles.
Take the highway 495 (Washington D.C. beltway) exit (exit 27) west, toward Silver Spring for 0.6 miles.
Take the highway 95 south exit (exit 25) on the left toward route 1 (College Park) for 1 mile.
Take the route 1 south (Baltimore Avenue) exit (exit 25B) toward College Park for 1.1 miles.
Turn right onto route 1 south (Baltimore Avenue).
     At University Boulevard/Greenbelt Road (route 193) turn right (west).
     At Azelea Lane/Paint Branch Drive/Metzerott Road, turn left (southeast) and drive onto campus.
     Pass University Boulevard/Greenbelt Road (route 193). Turn right (west) onto Campus Drive, at the brick entrance.
Notes: About 42 minutes from Arbutus in light traffic.

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