Science & Math

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

Overtime

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

Victoria Crater, on Mars. The black dot on the rim, at about the 10 o’clock position, is the Mars rover Opportunity. Expected to fail after 90 days, it has been exploring faithfully for more than three years.

Not So Fast

n2n + 41 produces prime numbers for all integers from 0 to 40 — but it fails when n equals 41.

Suburban Physics

http://commons.wikimedia.org/wiki/Image:Balloons-aj.svg

You’re driving a car. The windows are closed. In the back seat is a kid holding a helium balloon.

You turn right. You and the kid sway to the left. What does the balloon do?

Click for Answer

Math Notes

25 × 92 = 2592

Math Notes

13 + 53 + 33 = 153

The Beverly Clock

In the foyer of the Department of Physics at New Zealand’s University of Otago is a clock that has been running continuously since 1864. The “Beverly Clock” is driven by variations in atmospheric pressure and by daily temperature variations, so it never needs winding.

Relax

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

On March 23, 1989, a 1,000-foot asteroid missed the Earth by 400,000 miles.

If it had passed 6 hours earlier it would have struck us, creating the largest explosion in recorded history.

Math Notes

42 = 24

Math Notes

(27/8)9/4 = (9/4)27/8

Tee Time

http://commons.wikimedia.org/wiki/File:Apollo_14_Shepard.jpg

The last golf shots on the moon were taken by Apollo 14 astronaut Alan Shepard in February 1971.

When the crew returned to Earth, they received the following telegram from the Royal and Ancient Golf Club in Scotland:

Warmest congratulations to all of you on your great achievement and safe return. Please refer to the Rules of Golf section on etiquette, paragraph 6, quote – before leaving a bunker a player should carefully fill up all holes made by him therein, unquote.

Reductio Ad Absurdum

Forget everything you know about reducing fractions — it turns out you can just cancel individual digits:

reducing fractions

Not convinced?

reducing fractions
reducing fractions

This would have made fifth grade so much easier …

Erdös Numbers

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

Hungarian mathematician Paul Erdös was immensely prolific — he published about 1,500 articles in his lifetime. His influence is so great that his colleagues have taken to assigning “Erdös numbers” to one another. Erdös himself gets an Erdös number of 0; his direct collaborators get a 1; anyone who collaborates with them gets a 2, and so on.

Those in the first rank include many of the world’s top mathematicians, but there’s one standout: Hank Aaron. The Baseball Hall of Famer once signed a baseball with Erdös while accepting an honorary degree — and that, some say, counts as a joint publication.

Counting the Days

Thomas Fuller, known as the Virginia Calculator, was stolen from his native Africa at the age of fourteen and sold to a planter. When he was about seventy years old, two gentlemen, natives of Pennsylvania, viz., William Hartshorne and Samuel Coates, men of probity and respectable characters, having heard, in travelling through the neighborhood in which the slave lived, of his extraordinary powers in arithmetic, sent for him and had their curiosity sufficiently gratified by the answers which he gave to the following questions: First, upon being asked how many seconds there were in a year and a half, he answered in about two minutes, 47,304,000. Second: On being asked how many seconds a man has lived who is 70 years, 17 days and 12 hours old, he answered in a minute and a half 2,210,500,800. One of the gentlemen who employed himself with his pen in making these calculations told him he was wrong, and the sum was not so great as he had said — upon which the old man hastily replied: stop, master, you forget the leap year. On adding the amount of the seconds of the leap years the amount of the whole in both their sums agreed exactly.

– E.W. Scripture, “Arithmetical Prodigies,” American Journal of Psychology, 1891

Math Notes

(4 + 9 + 1 + 3)3 = 4913

(1 + 9 + 6 + 8 + 3)3 = 19683

Three Strikes

Predictions by Scottish mathematician and physicist Lord Kelvin, president of the Royal Society:

  • “X-rays will prove to be a hoax.” (1883)
  • “Heavier-than-air flying machines are impossible.” (1895)
  • “Radio has no future.” (1897)

Speaking to the British Association for the Advancement of Science in 1900, he said, “There is nothing new to be discovered in physics now; all that remains is more and more precise measurement.” Einstein’s annus mirabilis came five years later.

Where’s the Fallacy?

pound fallacy

The Ones Factory

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

Alcohol Problem

http://www.sxc.hu/photo/5607

Fill one glass with wine and another with water. Transfer a teaspoonful of wine from the first glass into the second. Then transfer a teaspoonful of that mixture back into the first glass. Now, is there more wine in the water or water in the wine?

Most people will predict it’s the former, but in fact the two quantities will always be the same. Can you see why?

Oops

http://commons.wikimedia.org/wiki/Image:European_starling.jpg

In 1890, a well-intentioned New Yorker named Eugene Schieffelin released 80 starlings in Central Park. He wanted to introduce every bird mentioned the works of William Shakespeare into the United States. (In The First Part of King Henry the Fourth, Hotspur says, “Nay, I’ll have a starling shall be taught to speak nothing but ‘Mortimer.’”)

He should have reconsidered. Scientists estimate that those birds have multiplied into more than 200 million in North America, where the starling has become a major pest, outcompeting other birds for nest holes. Opponents of genetically modified organisms still point to Schieffelin’s act to warn of the dangers of invasive species.

Geometry Disproves Arithmetic

geometric fallacy

The first figure, measuring 5 by 5, can be reassembled to form the second, measuring 8 by 3. Thus 25 equals 24.