Mathnasium's Word Problem of the Week - Amazing Norman

Zoom zoom! We're back with another installment of Word Problem Wednesday! Solve our bicycle-themed word problem below and follow along below for the answer!

Norman has a bicycle with wheels that measure 28 inches in diameter. How far will the bicycle go if the wheels rotate 100 times? (Round π to 3.14 to solve this problem.)

We love pi. Its quirky value fits memorably as date (March 14) that is celebrated and commercialized. However, Pi-Day is a recent invention. It was only started in 1988 by Larry Shaw, a physicist at the San Francisco science museum who looked at the calendar and made the connection, March 14, Pi-Day! And ordered pie for his staff, and thus this great mathematical tradition was borned.

The name “pi” should be easy to remember because its wonderful name fortunately coincides with the word “pie” (typically circular) and more importantly alludes to it’s relationship with circles. While humanity has known about pi and it’s value 3.14 for over 4000 years (that’s 2000 years BC!), it was only in 1706 that the Welsh mathematician William Jones first called it “pi”. He named it after the Greek word perimitros which means “perimeter”, the length of the outer edge of a shape. Perimeter is derived from the Greek words “peri” meaning outer and “meter” meaning measure (which you can easily remember as the “meter” used for measurements!). The Latin equivalent of “perimeter” for a circle is “circumference” derived from “circum” meaning “around” and “ferre” for carry, hence think about carry or walking around the circle! Either word is the measure or length of the outer edge but “circumference” specifically is perimeter of a circle.

The small Greek letter π is “pi” and that’s what we use as the representation of its numeric decimal value 3.14159265359… that just keeps on going (it's irrational)! You should think of π as just another number just like the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Most of us only think about numbers as only composed of digits 0 to 9 but that is so very limiting. So, for example, the number 100π is the same as the expanded number 314.159265359… that just keeps on going (how irrational). Keeping π as π is so much more concise, meaningful, and absolutely exact! We have many other special numbers in addition to π and it’s best to keep these special numbers unexpanded until we truly need their numerical value.

But what is π? Well, π is the ratio of the [measures of] circumference (C) of a circle to its diameter (D), or in concise mathematical notation π = C/D. It transpires that regardless of the size of a circle, that ratio is always the same, that's why it's special!

To remember that π = C/D, know that π > 1, and since the circumference is visibly longer than the diameter, the ratio C/D > 1 hence π = C/D. Or if you prefer remembering C = πD, that means that the circumference is a little over 3 times the diameter, and to be exact, the circumference is π times the diameter!

Norman’s bicycle wheel is 28 inches in diameter, that means, the circumference of the wheel is C = πD = 28π. That means for a single rotation, the wheel travels 28π inches. So, for 100 rotations, the wheel travels 28π ×100 ≅ 28 ×3.14 ×100 ≅ 8,790 inches ≅ 732 feet. Way to go Norman!

Photo from: http://inhabitat.com/watch-this-amazing-video-of-norman-the-bike-riding-...

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Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
201-969-6284 (WOW-MATH), fortlee@mathnasium.com
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