Have you ever thought about Pi? No, not Grandma's apple pie or blueberry pie, the
number Pi. Pi in a very interesting number, in this blog you will get to explore moreabout pi, what it is, and it's relationship to circles. Check it out.
Pi is often written using the symbol and is pronounced "pie", just like the dessert, the ratio of the circumference to the diameter of a circle is approximately equal to 3.14159265358979323846...
How many digits are there? Does it ever end? Because Pi is known to be an irrational number it means that the digits never end or repeat. But calculating the digits of Pi has proven to be an fascination for mathematicians throughout history. Some spent their lives calculating the digits of Pi, but until computers, less than 1,000 digits had been calculated. In 1949, a computer calculated 2,000 digits and the race was on. Millions of digits have been calculated, with the record held (as of September 1999) by a supercomputer at the University of Tokyo that calculated 206,158,430,000 digits. WOW!
How can I visualize this? Essentially what does it MEAN?
How many digits are there? Does it ever end? Because Pi is known to be an irrational number it means that the digits never end or repeat. But calculating the digits of Pi has proven to be an fascination for mathematicians throughout history. Some spent their lives calculating the digits of Pi, but until computers, less than 1,000 digits had been calculated. In 1949, a computer calculated 2,000 digits and the race was on. Millions of digits have been calculated, with the record held (as of September 1999) by a supercomputer at the University of Tokyo that calculated 206,158,430,000 digits. WOW!
The animation below shows how the circumference of a unit circle with diameter 1 is approximately
Soooo What's The Deal With The History of Pi??? MAKE IT SIMPLE!
ACTIVITIES YOU MAY ENJOY
3.14159265358979323846... BUT REMEMBER, IT WOULD WORK FOR ANY CIRCLE.
Soooo What's The Deal With The History of Pi??? MAKE IT SIMPLE!
Ok I will! Weellllll, ancient civilizations knew that there was a fixed ratio of circumference to diameter that was approximately equal to three. The Greeks refined the process and Archimedes is credited with the first theoretical calculation of Pi.
- In 1761 Lambert proved that Pi was irrational, that is, that it can't be written as a ratio of integer numbers.
- In 1882 Lindeman proved that Pi was transcendental, that is, that Pi is not the root of any algebraic equation with rational coefficients. This discovery proved that you can't "square a circle", which was a problem that occupied many mathematicians up to that time.
- An English mathematician named Wallis’s (c. 1650) expressed the π as the limit of an infinite product:
- Leibnitz’s in Germany, (c. 1674) expressed the value of π as an infinite alternating sum as show below:
Π = 4 (1 – 1/3 + 1/5 – 1/7 + …)
- Archimedes calculated that Pi was between 3 10/71 and 3 1/7. Is this a good approximation? How far off is it from what we know pi to be today? Is 355/113 is a better approximation?
Where Can I Find More Information About Pi? I'm SOOO Excited and into MATH!
Pi continues to be a fascination of many people around the world. If you are interested in learning more, there are many web sites devoted to the number Pi. There are sites that offer thousands, millions, or billions of digits, pi, clubs, pi music, people who calculate digits, people who memorize digits, Pi experiments and more. Check this Yahoo page for a some great listings.
- http://www.gizagrid.com/maths.html
- http://www.joyofpi.com/pilinks.html
- http://en.wikipedia.org/wiki/Pi
ACTIVITIES YOU MAY ENJOY
- One of the most interesting ways to learn more about Pi is to do pi experiments yourself. Here is a famous one called Buffon's Needle. In Buffon's Needle experiment you can drop a needle on a lined sheet of paper. If you keep track of how many times the needle lands on a line, it turns out to be directly related to the value of Pi.
If you can't memorize the numbers of pi like some people, perhaps it'd be simpler to come up with mnemonics to help remember the number pi to several decimal places.
Since pi is 3.14159265358979323846... but we don't easily remember that, the idea is to make a sentence in any language where the first word has 3 letters, the second has one, the third has four letters, ... etc. If you make the sentence yourself you are likely to remember it :)
For example:
- See, I have a rhyme assisting my feeble brain,its tasks sometimes resisting. Do you see how the words are related to pi?
- French:Que j'aime a faire apprendre Un nombre utile aux sages! Glorieux Archimede, artiste ingenieux,Toi, de qui Syracuse loue encore le merite! [Translation: I really like teaching a number, that is useful to wise men ! Glorius Archimedes, ingenious artist, You, of whom Syracuse still honors the merit !]
Can you come up with your own mnemonic it should be at least 7 words long. Click to see the longest mnemonic for pi ever made; it is a story!
WHAT TO DO???
- POST YOUR PI MNEMONIC OR POST LYRICS TO A SONG FOR PI
- DISCUSS 1 THING YOU LEARNED NEW ABOUT PI
- POST AN INTERESTING PI DISCOVERY ACTIVITY OR TID-BIT FOR YOUR FRIENDS
- REMEMBER POINTS WILL BE AWARDED TO STUDENT WHO COMPLETE HIGH QUALITY OF WORK
http://www.youtube.com/watch?v=nhlMHoEx8c4
ReplyDeleteI found a cool video of someone who converted the digits of pie into a piano melody. I don't play piano so I don't know if they did it right, but it sounds good! I didn't know how to post the true video, so here's the link.
I like how your blog first gives them the background information, and then lets the students explore pi on their own. This not only lets ensures that the students learn about pi, but allows them to incorporate their identities into the blog.
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