do I love thee? Let me graph the ways!
you come up with one or more equations to graph a heart on the coordinate
plane? The equations can be rectangular, polar, or parametric.
Can you shift your heart so the graph or its interior includes the point (2, 14)?
In the chart, color each square according to the clues below.
The Fibonacci sequence is shown below, with each term equal to the
sum of the previous two terms. If you take the ratios of successive
terms, you get 1, 2,
, and so on. But as you proceed through the sequence, these ratios get
closer and closer to a fixed number, known as the Golden Ratio.
1, 1, 2, 3, 5, 8, 13, …
Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?
Equations to solve in your
Is this a joke? Not if you can
multiply the first equation by 6,751 and the second by 3,249 in your head, and
not if you use a second, simpler method.
A 10 × 10 grid is painted
with three primary colors (red, yellow, and blue) and three secondary colors
(green, purple, and orange). The secondary colors are made by mixing equal
parts of the appropriate primary colors — that is, red and yellow are
mixed to make orange, red and blue to make purple, and yellow and blue to make
The figure at left shows
squares that were painted red and blue. No other squares were painted either
red or blue.
Suppose that each small
square requires a quart of paint. Altogether, 31 quarts of red paint, 40 quarts
of blue paint, and 29 quarts of yellow paint were used to paint the entire
10 × 10 grid.
Given this information, can
you determine if there were more yellow or purple squares? And how many more?
To the left is a circle
with an inscribed square. Obviously, there isn’t room for another
nonoverlapping square of the same size within the circle. But suppose that you
divided the square into n2
smaller squares, each with side length 1/n.
Would one of those smaller squares fit in the space between the large square
and the circle? As shown to the left, this works if n = 16 and the large square were divided into 256 smaller
squares. But it would work for smaller values of n, too.
What is the smallest value
of n such that one of the smaller
squares would fit between the larger square and the circle?
Label the ten points in the grid shown with the letters A-J so that
AB < BC < CD < … < HI < IJ.
A plywood sheet is 45 by 45
inches. What is the approximate diameter of the log the sheet was made from?
The diameter d of a circle equals ,
where C is the circumference, but
please do not make a mistake. The diameter of the log is not .