Meaning Of Pi (1949)

[Music] circle circle circles still not sure what pie means Maybe radius diameter circumference where does pie fit in here I just don't get it well let's look at these notes again circles are among the most important of geometric Concepts use them in Machinery in building in art for beauty and for utility yes what else did Mr Leonard tell us in math class about circles wheels are circles and wherever we have built moving machines from wagons to automobiles we have used wheels or circles to visit a shop where tools are used is to see many circles being put to many different uses for a circle is useful and it is beautiful but how does that help me to understand pi to understand circles we must study them let's begin by getting our term straight using a compass it is easy to draw a circle what are the terms to consider well the Center is the point around which the circle is described or drawn every point on that line is the same distance from the center any straight line from the circle to the center is a radius and any straight line through the center with its ends on the circle is a diameter the length of this line the circle line is the circumference and that's as far as I got before except I drew a lot more circles but what's this about high to understand circles means to be able to measure them and compare measurements go ahead John you can do it that yard stick ought to do the job now make a point in your circle so you'll know where you began to measure just roll your circle over the measuring stick until the arrow comes around again and you have the length of the circle or the circumference it's 31 and 716 in you can measure a circle after all it isn't hard to measure the diameter directly if measuring will do it well here I go and now you should know a lot about circles maybe even something about Pi you've measured a lot of circles this sprocket wheel with a DI diameter 8 1/2 in long has a circumference of 26 and 58 in but still what about Pi in studying the circumferences and diameters of circles you should notice something important circle with a diameter 2 in long of the circle is more than 6 in Long a circle with longer diameter a 3 in has a longer circumference too that's just common sense of course the longer the diameter the longer the circumference let's keep going I'm getting it suppose you take the circle with diameter of 3 in you place that Circle carefully you measure that you rotate the circle until you measure the circumference and you record these measurements then you measure another Circle this circle has a diameter of 1 in you carefully prepare to measure the circumference of this circle you find the circumference and you record these measurements these are the facts which have helped teachers of mathematics to develop the meaning of Pi I think I'm beginning to understand but not quite let's think of the facts in a different way suppose we think of the two circles at the same time our small circle with a 1in diameter our large circle with a 3-in diameter we know already the circumference of each of these circles now let's compare the length of the diameter of the small circle with its circumference we can see this compar compon by seeing how many diameters it takes to equal the circumference we can see that it takes three diameters and a little more to equal the circumference of the small circle what about the large Circle how many diameters will it take to equal the circumference of the large Circle once again we see it takes three diameters and a little more to equal the circumference is that true of all circles the three and a fraction diameters of any Circle equal the circumference of that Circle I should be able to answer that let's figure the ratio of those I've measured ratio of circumference to diameter my first measurement was circumference 31 and 716 in diameter 10 in 3 .1 3.14 well I guess that proves something they're all nearly the same every one of them you know that's quite a discovery the circumference is a little more than three times the diameter we usually use 3.14 as Pi H I didn't need to measure the circumference to find the circumference I could have just measured the diameter multipli by 3.14 and why couldn't I understand that when I read it before Pi mathematical the letter Pi denoting the ratio of the circumference of the circle to the diameter I'll bet I've read that a dozen times before and didn't know what it meant the ratio of the circumference to the diameter the value of this pi to 8 decimal places is 3.14159265 wow Pi can be RI in many ways all these are symbols for pi to find the numerical value of this important ratio was one of the great problems of history from the Old Testament it is evident that the Hebrews considered the value of pi to be exactly three the ancient Egyptians apparently had some knowledge of the value of piie but it was in Greece that the value of pi was more accurately determined and from the Greek alphabet comes the name the 16th letter of the ancient Greek alphabet is still used to name the relationship of the circumference of a circle to its diameter 3.1416 sometimes used as 3 and 17th as a matter of convenience pie that's what I discovered just now Circle a radius a diameter and [Music] pie the