PI is a number, represented by the symbol π. π=3.1416. What is this number used for? This number is the ratio of the circumference of a circle’s diameter. What the heck does that mean! Okay, the circumference is the distance around the outer edge of a circle. Now, the diameter is the distance across the middle of a circle. And in every case, the circumference of any given circle is approximately three times the diameter. If you are interested in calculating the ratio yourself, take the circumference of a circle and divide it by the diameter. Of course, you will have to have those numbers. But, you will find it to calculate to a decimal slightly larger then 3.14. Any size circle you calculate for the ratio you’ll find it equals 3.14.
That is pretty amazing, huh.
Important points and notes:
- circumference ≈ 3.14 x diameter
- It must be noted that 3.14 is an approximate and is a rounded off value of π.
That wasn’t very hard. Keep going. As we break it down you will find it is easy. You’ve got the idea of what PI is now, so what are you going to use it for?
What do we need PI for?
Come on now! In the first stage it is about finding the measurement around a circle. There are circles all around us. We need to be able to measure these circles for many reasons. It starts with a coin. A coin is round. We need to know the measurement of its circumference so we know what size to make the slots on the soda machines. If you have a car and you want to put cool tires and rims on it, you’ll need to know the total circumference of the rim and tire to make sure it fits your make and model. I think you’re getting the picture. This is not just for the mathematicians. And of course we need it for the bigger stuff like the circumference of the sun and the Earth. This is important stuff to scientist.
There are also other very important areas of math that PI is connected to. In case you are interested they are; continued fractions, logarithms of imaginary numbers (that sounds fun), and periodic functions. These are in advanced forms of mathematics. I would have to be really in the mood to get into those topics. But tonight I have a headache.
Some Fun Facts and Things to Know About PI:
- Did you know that π is the sixteenth letter in the Greek alphabet? It’s true. There must be an interesting connection here. I wonder if anyone has looked into it. If anyone knows, let us know.
- The exact value of PI cannot be calculated.
- In 1770, a German mathematician named Johann Lambert proved that PI (π) was irrational. I would be irrational too if I couldn’t find the answer.
- It was also proved by Ferdinand Lindemann in 1882 that PI (π) is transcendental. Transcendental means it goes on and on and on and on…………. Never ending.
- Example, 3.1416………………………. goes on and nobody knows where it ends.
- Around the middle of the 19th century, 707 decimal places were known.
- By the 20th century a computer was able to calculate it up to 100,000 decimal digits. It took the computer 8 hours to make this calculation.
- I would take a person working on a regular desk calculator, 8 hours a day, without errors, 30,000 years to reach the same calculation as a computer made in only 8 hours.
- 200,000,000,000 digits have been calculated and it still continues.
- An early Greek value for PI (π) was an approximation of 3 1/7. This was found by a very complex method that I do not wish to explain. Good Luck.
- π, does appear in many other mathematical formulas that have nothing to do with circles.
Main Point: PI (π) is the constant ratio of a circle’s circumference to its distance ( ).
Now, I have a question. If π never ends, does that mean that there are circles somewhere, that are bigger then anything we know, out there that measure the distance of the unknown digits of π? Wow, when I think of that idea, it makes me quiver.
PI Has History.
Who discovered PI? Know one knows who is responsible for giving us PI. But, we should thank them anyway. It is obvious that PI has been proven invaluable and personifies the essential important reality of the perfect geometric forms, such as the circle. The calculated number of PI (3.1416) is found in early historical mathematical records.
Fun Facts on the History of PI-
- Around 1800 b.c. to 1650 b.c.e., Babylonian clay tablets reveal how an area of a circle could be found from the circumference using a constant, the constant being equal to 3.125 or 3-1/8.
- Approx. 1650 b.c, The Rhind Papyrus refer to something similar to PI as being equal or about 3.16. But, this was in the context of a geometrical problem involving a square with the equal area of a given circle. That sounds interesting.
- Around 287 b.c.-212 b.c, Archimedes of Syracuse may have been the first to give a theoretical calculation of PI. He unequivocally related that the ratio of a circle’s circumference by the diameter. He proved his theory by using a series of polygons inscribed in a circle with another circumscribing it. He was able to figure that PI was less than or greater than or about 3.1418. Go Archimedes, Go Archimedes.
- (I Kings 7:23), “He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a circumference of thirty cubits to measure around it.” What does this mean? This suggests that the Ancient Hebrews, who built King Solomon’s temple, knew PI. This was around 1000 b.c. The math part is: Take the thirty and divide it by ten to get 3. Also keeping in mind that the word circumference is spelled with one extra letter, connecting that information with the fact that all Hebrew letters are also numbers, so if we take the ratio of the value of the word as it is written you get (111) to the normally spelled word that is (106), you will find a number of 1.047169811. Take this number and multiply it by 3 and you will get the amazing approximate of PI (π) = 3.141509434.
The Uniqueness of PI
What makes PI (π) so unique? Well, interestingly enough PI is not a unique number. Okay, this is where it gets really interesting. What does it mean that PI is not a unique number? Rational numbers can stand for a ratio or a common fraction, as we know them. PI cannot be turned into any common fraction, therefore, making it an irrational number.
Why and how does PI work for calculating the circumference of a circle?
First the why, it was found, no matter the measured diameter of a given circle, that when the circumference was divided by the diameter the result was always 3.14. Making 3.14 a constant quotient.
Second the how, it was found that the diameter is approx. a 3rd of the circumference of a circle. PI represents this ratio. So when we multiply this ratio by any given diameter it gives us the circumference of the given circle. This is really easy, isn’t it?
Now you know some of the basic ideas around the amazing number PI also known as π. Let’s take a break from the serious stuff and learn the fun side of PI.
If you divide the circumference of a pumpkin by its diameter, what will you have?
If you divide the circumference of the sun by its diameter, what will you have?
PI in the sky!
If you divide the circumference of a native Eskimo by his or her diameter, what will you have?
If you divide the circumference of a bowl of ice cream by its diameter, what will you have?
PI, a’ la mode.
PI is amazing and goes on and on…….
Many people are intrigued with PI. From about 4,000 years ago and up until now, people have been calculating and figuring how to find the most accurate values for PI. Now, they even have supercomputers calculating values for PI. So far, PI has been figured to contain over 1 billion digits and counting. There are also competitions for memorizing PI. PI is serious business. Through the years PI has been an interest and challenge to mathematicians and computer scientist. PI’s value is an amazing complex solution to a very simplistic problem: How does the circumference of a circle measures to its diameter?
Here is another interesting note on PI; PI, as it is written in the decimal number system, if written in the form of the binary system and with the right computer technological programming could be run to find different types of information, given the time and research. It could be amazing of what may be found. Could we hear PI or see PI? As it is a symbol of something that goes around continuously, could it be used to generate something? I am not a scientist, as it is I am not very good with math but something tells me PI is something big. Big and goes round!