Competition

Math

These examples illustrate how an interesting story may lead to a topic.

Musical Note Frequencies

In the 6th century BC, a Greek mathematician named Pythagoras conducted an experiment about the frequencies of different musical notes. He started with two strings. One string was exactly half the length of the other one. He plucked both strings, and discovered that the shorter string’s note was exactly one octave higher than the longer string’s note. This meant that an octave had a frequency ratio of 1:2. Ancient Greeks believed that a note sounded best when played with other notes whose frequencies were multiples of the first note. For example, a note with the frequency 220 Hz sounded best played with notes that were 440 Hz, 660 Hz, 880 Hz, and so on.

Thinking Questions: How has this discovery affected the way musicians compose music? What other mathematical principles apply to music and musical composition?

Other Possible Categories: Arts & Entertainment, Science & Technology

Nature’s Pattern

Does nature make sense? Leonardo Pisano believed so. Better known by his nickname, Fibonacci, this Italian mathematician, who lived from 1170 to 1250, revealed many patterns in nature. One such pattern is named after him; “the Fibonacci numbers” follow the sequence 1, 1, 2, 3, 5, 8, 13, 21, etc. Each successive number is the sum of the previous two numbers. The Fibonacci number pattern can be found over and over again in nature, in the reproduction patterns of rabbits, bees and many other creatures, and in the number of leaves, seeds, and growth segments of plants. Further, if you take two consecutive Fibonacci numbers and divide them, you obtain the “golden ratio”, also known as Phi. The golden ratio is fundamental to artistic concepts of perspective and beauty. It is evident in the Egyptians’ design of the pyramids, in the architecture of the ancient Greeks, and in the painting, sculpture and buildings of Renaissance Italy.

Thinking Questions: Where else does Fibonacci’s number pattern apply? Do you see the golden ratio in contemporary design? Are there other mathematical patterns in nature, and what might their significance be?

Other Possible Categories: Science & Technology, History & Government

Stock Markets

Did you know that you can own a little piece of a big company? In a stock market, people buy and sell shares of a company, known as stocks. People who own stocks are called “shareholders.” Companies sell stock because they want to raise money to expand their business—it costs lots of money to create new products, build more factories or stores, and hire more employees. People buy stock because they want to make money by investing. Some companies give part of their profits to shareholders by paying them cash, called “dividends.” Shareholders also make a profit by purchasing stock when the value is low and selling it when the value is higher. But, investing in the stock market can be risky. If the stock goes down in value, the shareholders lose money. Investors can buy stocks in many different kinds of companies and in many different markets around the world, such as the New York Stock Exchange in the United States, the London Stock Exchange in England, and the Nagoya Stock Exchange in Japan.

Thinking Questions: How and why do new Stock Exchanges develop? If it is simply a matter of buying low and selling high, why aren’t all investors successful? How can a number like a stock price represent the value of an entire company?

Other Possible Categories: Business & Industry

Citations

• Beer, Michael. “How Do Mathematics and Music Relate to Each Other?” Home page. 7 Oct. 1998. 3 Mar. 2004 <http://perso.unifr.ch/michael.beer/mathandmusic.htm>.
• Sommer, Sarah. “Pitch Differences.” Math and Music. 19 May 2003. 3 Mar. 2004
  <http://www.geocities.com/isymjazz/MathandMusicPage1>.
• Knott, Surrey. “Fibonacci Numbers and Nature.” Fibonacci Numbers and the Golden Section. 28 Jun. 2005.
  <http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#fingers>.
• O'Connor, J.J. and E. F. Robertson. Leonardo Pisano Fibonacci. October 1998
  <http://www-groups.dcs.st and.ac.uk/~history/Mathematicians/Fibonacci.html>.
• “The Golden Section.” Phi – The Golden Number. 12 Jul. 2005. 1997 – 2005.
  <http://goldennumber.net/goldsect.htm>.
• “Understanding the Stock Market.” Young Investor. Columbia Funds Distributor, Inc. 20 Aug. 2004 <http://www.younginvestor.com/kids/investIt/articleUnderstand
  StockMarket.html>.
• “What is the stock market?” The Mint. Northwestern Mutual Foundation. 20 Aug. 2004 <http://www.themint.org/investing/ whatisthestockmarket.php>.