Prof. Marjorie Senechal - "Quasicrystals Gifts to Mathematics"

Prof. Marjorie Senechal
Smith College
"Quasicrystals Gifts to Mathematics"
Jan. 12,2011

Six Ways to Sum a Series

http://www.maa.org/pubs/calc_articles/ma045.pdf

Riddle-Poems, and How to Make Them

http://catb.org/~esr/riddle-poems.html

I am always at your side. To a slab my tail is tied And my eyes are both inside my belly. Tickle my back, one/two/three! Wisdom and folly are yours to see.


The Moon is my father,
the Sea is my mother;
I have a million brothers,
I die when I reach land.


A hoard of rings am I,
but no fit gift for a bride;
I await a sword's kiss.


A wonder on the wave / water became bone.
- Book of Exeter

Pascal Triangle: Can you explain the following result?

Row 0 : 1
Row 1 : 1    1
Row 2 : 1    2    1
Row 3 : 1    3    3    1
Row 4 : 1    4    6    4    1

Etc.


Take a row of Pascal's Triangle.
Write a second copy of the row below it and place 0.
Multiply each pair of numbers and
then sum these products.

For example,

1    1    0
0    1    1
----------------
0    2    0
0 + 2 + 0 = 2 (it is in row 2)

1    2    1    0
0    1    2    1
-------------
0    2    2    0
0 + 2 + 2 + 0 = 4 (in row 4)

1    3    3    1    0
0    1    3    3    1
----------------------
0    3    9    3    0
0 + 3 + 9 + 3 + 0 = 15 (in row 6)

1     4     6     4     1     0
0     1     4     6     4     1
-----------------------------
0    4    24    24    4    0
0 + 4 + 24 + 24 + 4 + 0 = 56 (in row 8)

etc.

"It's Nonconvergent!"

Futurama is back, with the below clip Infinite Benders having some fun math.

Mark Setteducati in WSJ

The Wall Street Journal has a great article about magician and inventor Mark Setteducati.

Squares

At squaring.com, Stuart Anderson has finished compiling the Order 29 Perfect Squares. I've made some findings from the Imperfect squares, for example that the Mrs. Perkins Quilt of size 1099 has order 27. Note the two squares of size 324 -- this square cannot be found directly from 3-connected graphs.

Math Puzzles

Big, Big, Big Book of Brainteasers

Some sample puzzles:

#162: On a standard QWERTY keyboard, find 3 consecutive letters that make an acute triangle.

#181: An 8 slice pizza was eaten by 4 people. No-one ate more than the other 3 combined, and everyone had a different number of slices. How many did each person eat?

#384: A 24-hour clock shows the time 01:23, where the digits are in an increasing arithmetic progression. In this case, they increasing with constant of 1. How many times in 24 hours will this property be seen?


http://www.mathpuzzle.com/

Palindrome

True or False: The only palindrome with a non-palindrome base is 10662526601 = 2201^3

Fermat number and Mersenne number

Can a Fermat number be the product of two Mersenne numbers?

Niccolo Tartaglia's claim

In 1556, Niccolo Tartaglia (1500–1557) claimed that the sums

1 + 2 + 4, 1 + 2 + 4 + 8, 1 + 2 + 4 + 8 + 16, . . .

stood successively for a prime number and a composite number.

Was he right?

A Curious Way to Test for Primes

http://frank.mtsu.edu/~dwalsh/mathmag302-303-walsh.pdf

Cartoons

The Super Power Numbers

Definition: A positive number is said to be super power when it is the power of at least two different positive integers.

The first few ones are: 1, 16, 64, 81, 256, 512, ...

16 = 4^2 = 2^4, 64 = 8^2 = 4^3, 81 = 9^2 = 3^4, etc.

Find others

Riddle #1

He who locks himself into the arms of Morpheus promptly at eventide, and starts the day before it is officially announced by the rising sun, excels in physical fitness, increases his economic assets and celebrates with remarkable efficiency. What common phrase is hidden in the complicated sentence above?