Norman windows

Houses have windows to let in the light and fresh air. The most common shape for a window is a rectangle, but you also see round windows and hexagonal windows and other creative shapes. A Norman window is made up of two geometric shapes a semicircle on top of a rectangle. One side of the rectangle is the same measure as the semicircle s diameter. Figure 19-10 shows two Norman windows. 

The areas of the two Norman windows in the preceding problem are different by almost 8 square feet — a fairly large difference. You may be surprised to know that the perimeters of these two windows aren t nearly so different. 

The Problem Which has the greater perimeter a Norman window with a 4-by-6-foot base or a Norman window with a 6-by-4-foot base ... 

The perimeter of a Norman window consists of the three sides of the rectangle and the circumference of the semicircle. The circumference of a full circle is found by multiplying the diameter by n. Because you only want half that area, you multiply half the diameter (the radius) by n. The Norman window with the base of 4 feet and sides of 6 feet has a semicircle with radius 2 feet, so the total perimeter is 4 + 6 + 6 +2ti = 16 + 2tt = 22.28 feet. The Norman window with the base of 6 feet and sides of 4 feet has a semicircle with radius 3 feet, so the total perimeter is 6 + 4 + 4 + 3tt = 14 + 3n 23.42 feet. The perimeters of these two windows differ by just a little over 1 foot. 

What if you want the area of the rectangular part of a Norman window to be equal to the area of the semicircular part This arrangement just may be more esthetically pleasing to you. 

The Problem How long should the base of a Norman window be if the two sides of the rectangle are 2 feet high and the area of the rectangle is to be equal to the area of the semicircle ... 

His bicycle is decorated like a Mr. Magoo version of a Norman Rockwell Santa sled. A plastic Rudolf the Red-Nosed Reindeer with a glowing cherry red nose is wired to the front. A transistor radio propped up in his basket blares Booker T. Thomas sits decked head to waist in the Santa costume from the store window. On his legs are the orange jogging pants from Chuck. 

Norman Slabs. A type of glass for stained windows it is made by blowing bottles of square section and cutting slabs of glass from the four sides. Normative Analysis. The calculated... 

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