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Science & Math

One-Sided Issue

http://commons.wikimedia.org/wiki/File:Recycle001.svg

The international symbol for recycling depicts a Möbius strip.

Do Animals Have Emotions?

In 1984, a pet kitten was given to Koko, the Stanford University gorilla who communicates through sign language.

She cared for it as a baby gorilla until December of that year, when the cat escaped from her cage and was run down by a car.

When her trainers told Koko what had happened, she gave the signs for two words.

They were “cry” and “sad.”

Ahem

The statement “no statements are true unless they can be proven scientifically” cannot be proven scientifically.

Not So Fast

31
331
3331
33331
333331
3333331
33333331

… are all prime, but 333333331 = 17 × 19607843.

Proof That 4 Equals 3

a + b = c

4a – 3a + 4b – 3b = 4c – 3c

4a + 4b – 4c = 3a + 3b – 3c

4(a + b – c) = 3(a + b – c)

4 = 3

Homework

http://www.sxc.hu/photo/648069

It’s been known since 1876 that 267-1 isn’t prime, but for decades no one knew what the factors were.

Then, at a meeting in 1903, mathematician Frank Nelson Cole gave an hourlong “lecture” in which he didn’t say a word. On one chalkboard he expanded the value of 267-1:

147,573,952,588,676,412,927

On another he wrote:

193,707,721 × 761,838,257,287

Then he multiplied those values by hand. The two boards matched. He had found the factors. Cole returned to his seat amid a standing ovation.

He later admitted that finding the factors had taken “three years of Sundays.”

Easy as Pi

Isaac Asimov proposed this mnemonic for a famous constant:

How I want a drink, alcoholic, of course, after the heavy lectures involving quantum mechanics!

Count the letters in each word and you’ll get 3.14159265358979.

Concentrated Yuck

The bitterest thing in the world is denatonium, a compound discovered by Scottish researchers in 1958. Most people find its taste unbearable even in dilutions of 10 parts per million.

A New York chemist once went home with a trace of denatonium saccharide on his lip. He kissed his wife and she almost threw up.

Math Notes

1 + 4 + 5 + 8 = 18
18 × 81 = 1458

1 + 7 + 2 + 9 = 19
19 × 91 = 1729

The Eye of Sauron

http://commons.wikimedia.org/wiki/File:Fomalhaut_with_Disk_Ring_and_extrasolar_planet_b.jpg

The Eye was rimmed with fire, but was itself glazed, yellow as a cat’s, watchful and intent, and the black slit of its pupil opened on a pit, a window into nothing.

That’s a quote from The Fellowship of the Ring, but this image is actually a star. Fomalhaut, 25 light-years away, is one of the brightest stars in the night sky.

Draw your own conclusions.

DCLXVI

Hexakosioihexekontahexaphobia is fear of the number 666, which is linked to Satan and the Antichrist in the Book of Revelation.

Unfortunately, it’s rather hard to avoid. 666 is the sum of the squares of the first seven primes:

666 = 22 + 32 + 52 + 72 + 112 + 132 + 172

Also:

666 = 1 + 2 + 3 + 4 + 567 + 89

= 123 + 456 + 78 + 9

= 9 + 87 + 6 + 543 + 21

= 13 + 23 + 33 + 43 + 53 + 63 + 53 + 43 + 33 + 23 + 13

In 1989, after his second term as president, Ronald and Nancy Reagan moved to a new home in the Bel-Air section of Los Angeles. They had the address, 666 St. Cloud Road, changed to 668 St. Cloud Road.

Math Notes

102 + 112 + 122 = 132 + 142

More Magic

If this magic square worked upside down, this one works when reversed, “mirrorwise”:

96 64 37 45
39 43 98 62
84 76 25 57
23 59 82 78
54 73 46 69
26 89 34 93
75 52 67 48
87 28 95 32

Fancy That

31415926535897932384626433832795028841 is a prime number.

It’s also the first 38 digits of pi.

“Self-Locating” Strings

In the decimal expansion for pi, the digits 16470 appear in position 16,470.

And the digits 44899 appear in position 44,899.

Math Notes

37 = 32 + 72 – 3 × 7 = (33 + 73)/(3 + 7)

Cosmic Irony

http://commons.wikimedia.org/wiki/File:61-MR4-76.jpg

In 1961, astronaut Gus Grissom nearly drowned after a splashdown when his Mercury capsule opened prematurely. He recommended making the hatch more secure.

Eight years later he died when Apollo 1 caught fire. The hatch had prevented his escape.

Versatile

What’s unusual about this magic square?

18 99 86 61
66 81 98 19
91 16 69 88
89 68 11 96

It works just as well upside down:

96 11 89 68
88 69 91 16
61 86 18 99
19 98 66 81

From Royal V. Heath, Scripta Mathematica, March-June 1951.

Juvenile Chemistry

http://commons.wikimedia.org/wiki/File:Arsole-3D-vdW.png

This compound, C4H5As, is known as arsole.

When it’s fused to a benzene ring, it’s called benzarsole.

No, I’m not above pointing that out.

Math Notes

371 = 33 + 73 + 13

Math Notes

5882 + 23532 = 5882353

The Haberdasher’s Problem

Can you make three cuts in a square of cloth and rearrange the pieces to form an equilateral triangle?

Fallow and Fertile

http://commons.wikimedia.org/wiki/File:D%C3%BCrer_Melancholia_I.jpg

http://commons.wikimedia.org/wiki/File:Albrecht_D%C3%BCrer_-_Melencolia_I_(detail).jpg

Albrecht Dürer’s Melancholia I might brood about thwarted creativity, but it contains one of the most brilliant magic squares in all of European art.

You can reach the sum of 34 by adding the numbers in any row, column, diagonal, or quadrant; the four center squares; the four corner squares; the four numbers clockwise from the corners; or the four counterclockwise.

As a bonus, the two numbers in the middle of the bottom row give the date of the engraving: 1514.

Math Notes

0588235294117647 × 1 = 0588235294117647
0588235294117647 × 8 = 4705882352941176
0588235294117647 × 3 = 1764705882352941
0588235294117647 × 2 = 1176470588235294
0588235294117647 × 7 = 4117647058823529
0588235294117647 × 5 = 2941176470588235
0588235294117647 × 9 = 5294117647058823
0588235294117647 × 6 = 3529411764705882
0588235294117647 × 4 = 2352941176470588