Science & Math

A Mathematical Limerick

math limerick

The integral z-squared dz
From one to the cube root of three
Times the cosine
Of three pi over nine
Equals log of the cube root of e.

Math Notes

144648 = 861 × 168 = 492 × 294

185472 = 672 × 276 = 384 × 483

9949716 = 2583 × 3852 = 1476 × 6741

16746912 = 2556 × 6552 = 4473 × 3744

The Goldbach Conjecture

Every even number is the sum of two primes.

Is that true? No one knows. Originally proposed in 1742, it’s been tested as far as 1018, but the jury’s still out.

Black Tie Optional

http://en.wikipedia.org/wiki/Image:Crystal_palace_iguanodon.gif

English biologist Richard Owen designed a collection of life-size concrete dinosaurs for London’s Crystal Palace.

On New Year’s Eve 1853, he hosted a dinner for 21 inside the iguanodon.

Live and Let Die

James Bond never really explains why he likes his martinis “shaken, not stirred,” so in 1999 the University of Western Ontario’s biochemistry department decided to find out.

They discovered that a shaken gin martini has stronger antioxidant properties than a stirred one — which would help Bond avoid cardiovascular disease, stroke, and cataracts.

In their writeup for the British Medical Journal, they conclude, “007’s profound state of health may be due, at least in part, to compliant bartenders.”

See also Silly Old Bear.

A Self-Descriptive Number

In the number 6210001000:

  • The digit 0 occurs 6 times
  • The digit 1 occurs 2 times
  • The digit 2 occurs 1 time
  • The digit 3 occurs 0 times
  • The digit 4 occurs 0 times
  • The digit 5 occurs 0 times
  • The digit 6 occurs 1 time
  • The digit 7 occurs 0 times
  • The digit 8 occurs 0 times
  • The digit 9 occurs 0 times

See also The Quick Brown Fox …

Math Notes

115132219018763992565095597973971522401 = 139 + 139 + 539 + 139 + 339 + 239 + 239 + 139 + 939 + 039 + 139 + 839 + 739 + 639 + 339 + 939 + 939 + 239 + 539 + 639 + 539 + 039 + 939 + 539 + 539 + 939 + 739 + 939 + 739 + 339 + 939 + 739 + 139 + 539 + 239 + 239 + 439 + 039 + 139

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.