Question from Daniel,
Would you explain problem 12 from lesson 14.5? How exactly do you calculate circular inches?
First, a circular inch is the amount of area taken up by a circle one inch in diameter.
So that makes one circular inch = Area = pi*(d/2)^2
Looking to the square, from number 9 and 10, you can see the relationship between the ratio of two squares, and the definition of the area. Fact is, the square inch (one square with sides of a inch) is the unit of measure.
So likewise, the circle with diameter of 1 is the unit of measure.
All that might sounds confusing, but between 9 and 10 the same argument hold for 11 and 12.
In other words, the diameter of a circle IS how you measure circular inches. If it is 10 inches in diameter, the circle inches are 10 inches. If it is 30 inches in diameter, the circular inches are 30 inches.
He is just pointing out the definition.