Monday, August 18, 2014

A Piece of Pi


National Pi Day March 14th (3.14)

March 14th is "National Pi Day" because Pi is represented, rounded to the nearest hundredth, as 3.14.

Pi is also sometimes approximated as 22/7, or 3 and 1/7.

Pi is an irrational number that represents the ratio of the circumference of a circle to its diameter.
An irrational number is one that, no matter how many decimal places you take the number to, there will always be more decimal places you can take it to. Other examples of irrational numbers are square roots of numbers that are not perfect squares, like the square root of 2, 3 or 5. Any number that can be shown as a fraction is by definition a rational number.

The Circumference of a Circle

In order to figure out the circumference of a circle (this would be of help if you wanted to, say, put a ribbon around a cylinder), you multiply the length of the diameter (a diameter is a line from one end of the circle edge [circumference -- the thick magenta around the edge of the circle pictured here] to the other that passes through the center of the circle, like the magenta lines within the pictured circle) or twice the length of the radius (a radius is a line segment from the center of the circle to the edge of the circle) and multiply it by pi. As an estimate (pi is an irrational number, a number that has no exact value, so, to work with it, we must estimate), you can use either 3.14 or 22/7

In other words, if the diameter of a circle is 1, then the circumference is approximately 3.14 or 22/7; if the radius is 1 (then the diameter is 2), the circumference is 6.28 or 44/7 (or 6 2/7).

The Area of a Circle

To find the area of a circle, you square the radius (or 1/2 the diameter) and multiply it by pi.

For example, if the diameter is 2 (making the radius 1), 1 squared is 1, multiplied by pi is pi (or approximately 3.14 or 22/7). If the radius is 2, then 2 squared is 4, 4 times pi is about 12.56 or 88/7 or 12 4/7. If the radius is in inches, then the area is in square inches (so if the radius is 2 inches, then the area is 12.56 square inches).

Math and Me

Math has always been one of my "things". I've been tutoring math since I was in High School -- when I was a sophomore in high school (age 14), I started tutoring freshwomen (I went to an all-girl religious school) in Algebra. By my senior year, I was tutoring my own classmates (in elective senior math) along with lower classwomen. I still tutor math (and other subjects) and I still love algebra and geometry.

One of my recent tutees (who is in college now -- I tutored her from 6th to 11th grade and still work with her brother) used to ask me to create sample problems for her and then said the ones I created were harder than the ones in her book, so I said to her -- keep in mind, if you can do mine the test will be a snap -- she never again complained and always aced her tests.

Oh, BTW, one of my pet peeves is calculators. I don't allow my tutees to use them for anything that can be figured out without one. If you can do it without the calculator, doing it with the calculator should be easy, right? Well, not so much for me. When I was in grad school, I took a statistics class. During tests, I would have a pile of paper and do all the math that way. I would then check on my calculator (which I left in the corner) and if the numbers didn't match, I would redo on the calculator first (that was wrong more often than my figuring). I still managed to finish the test (and get a high A) before anyone else in the class. Never underestimate the power of your own brain.
Compugraph Designs on Printpop

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Compugraph Designs Arts Now Site

Arts Now is another “Print on Demand” site. They have a nice collection of clocks and watches, including the one pictured here (with my popular math symbols design on it). Click on the picture to see the entire site.

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