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>.
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