How mathematicians do it…

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Aerodynamicists do it in drag.

Algebraists do it by symbolic manipulation.

Algebraists do it in a ring, in fields, in groups.

Analysts do it continuously and smoothly.

Applied mathematicians do it by computer simulation.
Banach spacers do it completely.

Bayesians do it with improper priors.

Catastrophe theorists do it falling off part of a sheet.

Combinatorics do it in as many ways as they can.

Complex analysts do it between the sheets

Computer scientists do it depth-first.

Cosmologists do it in the first three minutes.

Decision theorists do it optimally.

Functional analysts do it with compact support.

Galois theorists do it in a field.

Game theorists do it by dominance or saddle points.

Geometers do it with involutions.

Geometers do it symmetrically.

Graph theorists do it in four colors.

Hilbert spacers do it orthogonally.

Large cardinals do it inaccessibly.

Linear programmers do it with nearest neighbors.

Logicians do it by choice, consistently and completely.

Logicians do it incompletely or inconsistently.

(Logicians do it) or [not (logicians do it)].

Number theorists do it perfectly and rationally.

Mathematical physicists understand the theory of how to do it, but have difficulty obtaining practical results.

Pure mathematicians do it rigorously.

Quantum physicists can either know how fast they do it, or where they do it, but not both.

Real analysts do it almost everywhere

Ring theorists do it non-commutatively.

Set theorists do it with cardinals.

Statisticians probably do it.

Topologists do it openly, in multiply connected domains

Variationists do it locally and globally.

Cantor did it diagonally.

Fermat tried to do it in the margin, but couldn’t fit it in.

Galois did it the night before.

Mðbius always does it on the same side.

Markov does it in chains.

Newton did it standing on the shoulders of giants.

Turing did it but couldn’t decide if he’d finished.

Top 10 list of geeky math comics / webcomics

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I’m a math geek, so I enjoy reading the occasional comic strip that’s math-related. Here is my list of the top 10 webcomics/comics that I read on a regular basis:

1. Foxtrot – Surely, everyone knows this one. It occasionally has a lot of math humor but is currently on a Sunday only publication schedule.

2. xkcd – Updated every Mon, Wed, Fri, and a very popular webcomic online.

3. Abstruse Goose – Funny webcomic updated regularly, but often physics related as well.

4. Spiked Math – New daily webcomic in color (this should be on the top of the list since I created it ;-))
5. (x, why?) – A funny webcomic, and has over 350 comics published to date.

6. Brown Sharpie – Updated every Mon, Wed, Fri, and can be quite humorous.

7. Brightly Wound – Often contains physics and astronomy as well.

8. twisted pencil – Usually updated Tue/Thu and contains lots of puppets.

9. mathTICS
– Usually has some pretty funny strips. Not sure if the author is as
active right now and the archive only has the first 100 strips.

10. Indexed – Interesting concept. Mostly consists of Venn diagrams and graphs.

Funny Math Limericks

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There once was a number named pi
Who frequently liked to get high.
All he did every day
Was sitting in his room and play
With his imaginary friend named i.

There once was a number named e
Who took way too much LSD.
She thought she was great.
But that fact we must debate;
We know she wasn’t greater than 3.


A mathematician confided
That the M”Mobius band is one-sided
And you’ll get quite a laugh
If you cut one in half
‘Cause, it stays in one piece when divided.


A mathematician named Klein
Thought the M”Mobius band was divine
Said he: If you glue
The edges of two
You’ll get weird bottles like mine.


There was a young fellow named Fisk,
A swordsman, exceedingly brisk.
So fast was his action,
The Lorentz contraction
Reduced his rapier to a disk.


‘Tis a favorite project of mine
A new value of pi to assign.
I would fix it at 3
For it’s simpler, you see,
Than 3 point 1 4 1 5 9


Pi goes on and on and on …
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?


If (1+x) (real close to 1)
Is raised to the power of 1
Over x, you will find
Here’s the value defined:


Integral z-squared DZ
from 1 to the cube root of 3
times the cosine
of three pis over 9
equals log of the cube root of ‘e’.


A burlesque dancer, a pip
Named Virginia, could peel in a zip;
But she read science fiction
and died of constriction
Attempting a Moebius strip.


A conjecture both deep and profound
Is whether the circle is round;
In a paper by Erdo”s,
written in Kurdish,
A counterexample is found.


There once was a log named Lynn
Whose life was devoted to sin?
She came from a tree
Whose base was shaped like an e?
She’s the most natural log I’ve seen.


Hilarious Math Pick-up Lines

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I wish you were my calculator so I could plug my natural log into you.

I wish I was sin^2(x) and you were cos^2(x), so together we could be 1.

I wish our dot product were 0 so my vector could be normal to your unit circle.

I want to be a derivative so I can be tangent to your curves.

Why don’t you be the numerator and I be the denominator and both of us reduce to the simplest form?

How can I know so many hundreds of digits of pi and not the digits of your phone number?

Ever wonder what L’Hopital’s rule has to say about limits in the form of me over you?

Baby, can I be your integral, so I can be the area underneath your curves.

Can I plug my solution into your equation?

The volume of a generalized cylinder has been known for thousands of
years, but you won’t know the volume of mine until tonight.

The Trachtenberg Speed System

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Who was Trachtenberg?

  • Professor Jakow Trachtenberg was the founder of the Mathematical Institute in Zurich, Switzerland.
  • He was a Russian, born June 17th, 1888, and studied engineering.
  • While still in his early twenties, he became Chief Engineer with 11,000 men under his supervision.
  • After the Czar of Russia was overthrown, he escaped to Germany where he became very critical of Hitler. He was later imprisoned.
  • Most fellow prisoners around him gave up hope and died even before being sent to their death. He realized that if he wanted to stay alive, he had to occupy his mind with something else rather than focus on the hopeless conditions surrounding them. He set his mind on developing methods to perform speed mathematics.
  • With the help of his wife, he escaped from prison and fled to Switzerland.
  • There, he taught his speed math system to young children. It was very successful.

Trachtenberg developed a set of rules (algorithms) to multiply long numbers by numbers from 0 to 12. These rules allow one to dispense with memorizing multiplication tables if that is desired.
Even better, it gives a way to help memorize them, by allowing one to
work out the answer by rule if one cannot remember it by rote. We
perform each rule starting at the far right. The `number’ is the digit
of the multiplicand just above the place that we are currently
computing. The `neighbor’ is the digit immediately to the right of the
`number’. When there is no neighbor, we assume it is zero. We also
write a zero in front of the multiplicand.

Note that the following rules only use the operations of addition, subtraction, doubling, and `halving’.


Download the file trach.pdf for some examples. Also see the book: Trachtenberg, Jakow (1960). The Trachtenberg Speed System of Basic Mathematics. Doubleday and Company, Inc.

Speed Math via Vedic Mathematics

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Vedic mathematics is based on sixteen sutras which serve as somewhat cryptic instructions for dealing with different mathematical problems. Below is a list of the sutras, translated from Sanskrit into English. They were presented by a Hindu scholar and mathematician, Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja, during the early part of the 20th century.

  1. By one more than the previous one
  2. All from 9 and the last from 10
  3. Vertically and crosswise (multiplications)
  4. Transpose and apply
  5. Transpose and adjust (the coefficient)
  6. If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero
  7. By the Para-party rule 
  8. If one is in ratio, the other one is zero.
  9. By addition and by subtraction.
  10. By the completion or non-completion (of the square, the cube, the fourth power, etc.)
  11. Differential calculus
  12. By the deficiency
  13. Specific and general
  14. The remaining by the last digit
  15. The ultimate (binomial) and twice the penultimate (binomial) (equals zero)
  16. Only the last terms
  17. By one less than the one before
  18. The product of the sum
  19. All the multipliers

The first one is basically the multiplication algorithm by 11 discovered independently by Trachtenberg.

Let us look at the second one, which is used quite a bit in Vedic Mathematics: All from nine and the last from ten.

subtracting from a large power of ten with many columns of zeros, it is
not necessary to write the notation for borrowing from the column on
the left. One can instead subtract the last (rightmost) digit from 10
and each other digit from 9. For example:


the method is also used when finding the deficit from the next larger power
of ten when setting up a multiplication problem using the
cross-subtraction method.

The third one is Vertically and crosswise (multiplications). One use for this is for multiplying numbers close to 100.

you want to multiply 88 by 98. Both 88 and 98 are close to 100. Note
that 88 is 12 below 100 and 98 is 2 below 100. This can be pictured as


subtract crosswise to get the first two digits of the answer. It
doesn’t matter if we do 88-2=86 or 98-12=86, both give the same number.
To get the last two digits we multiply vertically: 12 x 2=24.
Therefore, the answer is 8624.

The same strategy works for
multiplying two numbers above 100. For example, 107 times 111. Quickly
we add the surplus from 107 (which is 7) to 111 to get 118, the first 3
digits of the answer. To get the last two digits, we multiply the
surplus of 107 from 100 by the surplus of 111 from 100: namely, 7 x
11=77. Thus, the answer is 11,877.

Vedic Mathematics is all about using different formulas in a variety of ways.
In the above rule we are using:
The above notation is short for:
and is often used since it’s easier to see what the number actually is.

above generalizes for numbers close to a base of 1000. Note that the
second sutra becomes quite useful for when you are computing the
deficit from the base.

Math Grape Jokes

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Q: What’s purple and commutes?
An Abelian grape.

Q: What is purple and all of its offspring have been committed to institutions?
A simple grape, it has no normal subgraphs.

Q: What is lavender and commutes?
An Abelian semigrape.

Q: What’s purple, commutes, and is worshipped by a limited number of people?
A finitely-venerated Abelian grape.

Q: What’s purple, round, and doesn’t get much for Christmas?
A finitely presented grape.

Using Fibonacci for mile <--> km conversion

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The Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …
can be used to convert miles to kilometers (and vice versa). For example, to find how many km 5 miles is, take the next Fibonacci number which happens to be 8. Thus, 5 miles is approximately 8 km. Similarly, 8 miles is approximately 13 km, and so on.

This works because the growth rate of the Fibonacci numbers converges to the golden ratio (approx 1.618) which happens to be very close the km/mile conversion (1 mile = 1.609 km).