# Pi Fights in Court

March 3, 2014 and March 14. 3.14. Both are Pi Day.

How often has Pi come up in case law? The answer is equal to, but not less than, 3 times (and not 3.14). Here are the cases with math:

Pi used to determine the 200 foot zones of protection based on the radii from wellheads or wellfields:

where Q =permitted average dailyflow from the well (measured in cubic feet per T = five years (1825 days);

3.14 = mathematical constant pi;

r =radius (feet);h =distance from the top of the producing aquifer to the bottom of the hole;

n =effective porosity.

Adam Smith Enters. v. State Dep’t of Envtl. Regulation, 553 So. 2d 1260, 1263 (Fla. Dist. Ct. App. 1st Dist. 1989).

Pi was used in a zoning fight over the removal of a fence around a children’s day care:

In order to calculate the area of a circle which has a perimeter or circumference of 117 feet, one must first calculate the diameter. The diameter is calculated by dividing the circumference (117) by pi (which is approximately 3.14) which reveals a diameter of 37.26 feet. Next, the radius is calculated by taking 1/2 of the diameter (37.26) which yields a radius of 18.63 feet. The area of a circle is calculated by taking the radius squared or 347.07 multiplied by pi. The area of the circle is, therefore, 1,090 square feet.

Gronceski v. Town of Long Beach Bd. of Zoning Appeals, 721 N.E.2d 359, 365 (Ind. Ct. App. 1999).

Pi was used in finding whether a police officer was an expert witness for determining the speed of a car in an accident:

We have to find, before we can determine the speed of the vehicle, we have to determine the radius, which is an unknown fact. I will go over the entire formula. It equals speed or velocity of the vehicle, 3.9 is the mathematical constant. The most vivid example of the mathematical constant might be the factor pi, which received a designated value of 3.14, which you may remember from high school math in determining measurement with relation to circles.

Again, the square root sign, R is the radius, times of which represents the coefficent of friction, and the coefficient of friction, in very simple terms, is the slipperiness of the pavement.

State -vs- Greer, 1983 Ohio App. LEXIS 13849 (Ohio Ct. App., Cuyahoga County Aug. 4, 1983).

The number of cases using 3.14 in expert testimony likely goes on for infinity, especially in construction defect cases and zoning. These cases also highlight the danger of a juror saying, “It was my understanding there would be no math involved,” so please remember to include one math problem in your jury selection questionnaire.