Section 8.3 Individual Research
Prepare a classroom demonstration of topology by drawing
geometric figures on a piece of rubber inner tube. Demonstrate
to the class various ways in which these figures can be
distorted.
The problem shown in the News Clip was first published
by John Jackson in 1821. Without the poetry, the puzzle
can be stated as follows: Arrange nine trees so they occur
in ten rows of three trees each. Find a solution.
Celebrate the Millennium
a. Consider the product
(1)(2)(3) ... (1,998)(1,999)(2,000).
What is
the last digit?
b. Consider the product
(1)(2)(3) ... (1,998)(1,999)(2,000).
From the product,
cross out all even factors, as well as all multiples of
5.
Now, what is
the last digit of the resulting product?
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