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| 1.
Which of the following represents the square of any number n? |
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| 2.
What is i^2 (i squared)? |
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| 3.
Solve n^2 = n. Note: There are two answers. |
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| 4.
Which of the following can be made into a square with changes to its angles only? |
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5.
Everybody knows that each angle of a square is 90 degrees, right? Well, I just drew a square whose angles are each 120 degrees. Where did I draw it?
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6.
A number raised to the second power is a square, and a number raised to the third power is a cube. What term can be used for a square of squares, or a number raised to the fourth power?
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7.
If a solid object undergoes a proportional increase in size, which measure increases by the square of the multiplier?
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8.
Using only a compass and a straightedge, you try, in a finite number of steps, to make a square with the same area as a given circle. Don't try too long, because it can't be done! That this is a futile exercise was proven in 1882 with the Lindemann-Weierstrass theorem. What's the name of this famous problem?
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9.
In rectangular coordinates, what is the fourth vertex of a square whose other vertices are (1,1) (3,-1) (1,-3)?
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10.
Finally, you have 1475.366 feet of fencing and want to use it to enclose a quadrilateral fish farm for vermillion Clupea pallasii. The fish farm is to have the maximum possible area. What shape will the farm be?
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