We Lack Numeracy Skills

Alan Smith reported amazing statistics of adult numeracy:

2011 England Survey: 49 of 100 adults lacked of numeracy Level 1 skills (fractions, percentage, and decimals).  The figure is only shocking for 51% of population.

OECD reported (PIAACX2012) that forty percent of USA young people aged 16-19 were below Level 2.

This is statistics. Statistics is a part of mathematics and it is about us as a group.

There are two categories of people who can and who cannot do numbers.

Are You in a category of people who are comfortable with numbers? Check / train yourself at the website A+Click

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Pythagorean Triples Were Known 1,000 Years Before Pythagoras

The Babylonian clay tablet from the collection of Columbia University dating from 1,000 years before Pythagoras’s theorem is a trigonometric table which has 15 pairs of numbers forming Pythagorean triples: three whole numbers a, b and c:

a2 + b2 = c2

The tabet is known as the world’s oldest trig table. Babylonians used the base-60 numbers, which permitted many more accurate fractions than the contemporary base 10. For example, 2/3 = 0.6666… (or 40 minutes) was a finite number. The base-60 system were inspired from such shapes as a circle and the regular hexagon (see an example).

Mystic Number 7

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Why we frequently use number 7?

Why there are seven days of week? seven deadly sins? seven wonders? . . . .

Look for the answer in the night sky or at aplusclick.org

Why Is X The Unknown?

Terry Moore explains that the inventors of algebra were Arabic scientists. Their definition:

X = something, some undefined unknown thing = the unknown thing.

When the books were translated from Arabic to Spanish the Arabic unknown was “SH” that did not exist inSpanish. They replaced it by “X“.  It migrated to other European languages 600 years ago.

X is “X” because Spanish language does not have “SH“.

Cat, Rat, Hat, and Mat

 

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Mary has a cat, and a rat, and a hat, and a mat.

If the cat is on the mat, and rat is in the hat, but the hat is on the mat, where is the rat?

This is a simple puzzle asked by Leslie Green, who collects dozens challenging puzzles.  The collection of Leslie Logic and Math Puzzles is presented at the website Aplusclick. It’s worth to try the challenging questions.

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Selfie Math

Jim is going on a tour around the world. He has 5 tops, 4 bottoms, and 3 pairs of footwear. He wants to post a selfie everyday to show different places and his different outfits to his girl-friend Mary, who stays at home. He does not want to wear the same outfit twice. ## For how many days does he have enough clothing?

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Leslie Green gives the answer : 96 days.

Can you explain why it is 96? What is logic behind?

 

 

Beautiful Math Problems

What are characteristics of the most beautiful math problems?

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They are practical, they give an impression that the problem cannot be solved, and finish by an unexpected (surprise) solution.

It is not about the beautiful math equations or mathematical beauty. It is mostly about recreational math, brain teasers, and thinking outside the box.

Find a short list of my favourite beautiful problems:

1. Morozkin’s problem:

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Vladimir Arnold (1937-2010), one of the greatest 20th century Russian mathematicians told the following story:

“Our schoolteacher I. V. Morozkin gave us the following problem: Two old women started at sunrise and each walked at a constant (different) velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m.  At what time was the sunrise on this day?”

Solution

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2. Martin Gardner’s favorite problem

“Three sailors come across a pile of coconuts. The first sailor takes half of them plus half a coconut. The second sailor takes half of what is left, plus half a coconut. The third sailor also takes half of what remains, plus half a coconut. Left over is exactly one coconut, which they toss to a monkey. How many coconuts were in the original pile?”

Solution

3. Lucas problem

François Édouard Anatole Lucas (1842 – 1891) was a French mathematician.

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Every day at noon, a ship leave Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights. How many ships will a ship leaving Le Havre today meet at sea?

Solution

4. Euler bridge problem

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In a city Konigsberg, there were seven bridges. There was a tradition to walk and cross over each of the seven bridges only once. If a person starts and finishes at the same point, can he accomplish this task?

Solution

5. Secretary problem

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An entrepreneur wants to hire the best person for a position. He makes a decision immediately after the interview. Once rejected, an applicant cannot be recalled. He interviews N randomly chosen people out of 100 applicants, rejects them and records the best score S. After that, he continues to interview others and stops when the person has a score better than S. What number N do you recommend to the cruel man?

Solution

6. Monty Hall

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A venture capitalist will invest in only one of three start-up companies: A, B, or C. I will make a lot of money if I invest in the same company, and will lose all of my money if I choose another company. I decide to invest in company A and I inform the venture capitalist. He assures me that he does not invest in company C. What company do you recommend for me to make the investment?

Solution

7. The Legend of Carthage

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The Legend of Carthage: Queen Dido and her followers arrived in North Africa. The locals told them that they could have the coastal area that an ox hide would cover. She cut the hide into a series of thin strips, jointed them together, and formed a coastal shape. The ox-hide enclosed area was known as Carthage. If you had a 10 km long strip, which shape (rectangle, triangle, semi-circle, or semi-ellipse) would you choose to maximize the enclosed area?

Solution

8. Lewis Carroll’s Coaches

twotrainsA coach leaves London for York and another at the same moment leaves York for London. They go at uniform rates, one faster than the other. After meeting and passing, one requires sixteen hours and the other nine hours to complete the journey. What total time does each coach require for the whole journey?

Solution

You are welcome to expand the list by submitting your input at the website www.aplusclick.org