The following figure shows a cross-section of a nautilus shell with a superimposed polar coordinate grid. The outer spiral of the shell has been traced with a green curve. Our objective in this section is to determine a formula for the green curve by measuring the r coordinates of points on the curve and then fitting a formula to the measured points.
You may measure with a ruler marked with metric units (centimeters and millimeters) or with English units (inches and fractions of inches). These measurements may be done on your computer screen or on a printed copy of this page, whichever you find more convenient.
No matter how carefully you measure, your results will not be highly precise. First, the placement of the center of the grid is somewhat arbitrary. Second the green curve is a rough approximation of the outer curve of the shell. Third, the curve has been drawn with a rather thick line -- you should try to measure consistently to the center of the line.
If you cannot do measurements on the picture, either on screen or on a printed copy, click here.