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Rounding out pi is OK for calculating approximations

You wanted to know

"If pi is infinite, how come we can use it in math problems?" asked a student in Gregg Thompson's sixth-grade social studies class at Woodland Middle School in Gurnee.

Say your prized marble collection is stored in paper bags, but when the bags tip or rip, the marbles spill all over the floor.

"Clean it up," you're mom says - probably more than once - so you devised a unique storage system, tennis ball cans. They'll hold lots of marbles, they have a snug lid, and they're easily stored on the bookshelves.

How many tennis ball cans will neatly contain the marble collection?

There's a math formula that will help you figure out the volume inside one can. Once you know the volume, you can determine how many marbles will fit and then you can figure out the number of cans you need to store the entire collection.

The can is a cylinder - two circles connected by a tube. It turns out that all circles have the same width-to-circumference ratio. The circumference is the distance around the circle. This universal ratio is about 3-to-1, that is, the circumference is a teensy bit more than three times bigger than the diameter (width) of the circles.

The ratio is the same no matter the size of the circle - a pencil eraser, a trampoline, the planet Earth.

Mathematicians call this ratio pi, a Greek letter representing perimeter - and it's an infinite number. When the circumference is divided by the diameter, the result can go beyond 100,000 decimal points, so to make calculations easier, pi is rounded to 3.14, or shown as the symbol π.

Pi helps you calculate the area of the circle. To determine the volume (V) of the cylinder - use pi, half the diameter of one circle (r, or radius) two times (two circles) and the height (h). The formula is V=πr^2h.

Mathematics Professor Cristian Lenart at the University of Albany, New York, said experts use either 3.14 or pi shown as π.

"In concrete calculations, we use approximations of it, so there's only a finite number of decimals. For theoretical purposes, in calculations, we use pi as a symbol, so we don't get to effectively use the infinite number of decimals," Lenart said.

Lenart says pi is useful in many fields that use math.

"The original application of pi was to calculate lengths, areas, and volumes of geometric objects, but pi makes an appearance in many other areas of mathematics such as complex numbers obtained by introducing the square root of -1 and functions of a complex variable, probability and statistics, for instance, in relation to the normal distribution, chaos theory, etc.," Lenart said.

"The calculations are important in engineering, physics, chemistry, biology. Although not a physical constant, pi appears routinely in equations in physics and astronomy describing fundamental principles of the universe, due in no small part to the relationship between the universe and the nature of the circle."

Check it out

The Grayslake Area Library suggests these titles on Pi:

• "Pi," by Kevin Cunningham

• "Sir Cumference and the Dragon of Pi: A Math Adventure," by Cindy Neuschwander

• "Why Pi?" by Johnny Ball

• "Eat Your Math Homework: Recipes for Hungry Minds," by Ann McCallum

• "Train Your Brain to be a Math Genius," by Dr. Mike Goldsmith

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