Showing posts sorted by relevance for query Pi Day. Sort by date Show all posts
Showing posts sorted by relevance for query Pi Day. Sort by date Show all posts

Multicultural History of Pi

Mathematicians around the world celebrate the number pi on March 14 every year. This year is a very special year and is being called the pi day of the century because besides the date the year gives more digits of accuracy and if you look at time of the day to the second you can go nine digits after the decimal point for your celebration! Various celebrations are planned around the world including in Chicago, MIT in Cambridge, Massachusetts, Arizona, New Jersey, and San Francisco (where the first Pi Day Celebration was held).

Pi is a very special number in our world. It is a number that has been explored for thousands of years in just about every culture. Why? Because people wanted to learn about their world and started to realize that the same number kept appearing when taking the circumference of a circle (distance around the circle) and divide it by the diameter (distance across the circle through the center). The Babylonians and Egyptians were the first known to start the hunt for pi about 4000 years ago. Some say they figured out the ratio of a circle's circumference to diameter is slightly bigger than three or about 3 1/8. 

Mathematical Dates & Exponents -- Math Lesson

As I was listening to the radio today I heard the deejay talk about the special date today and I'll admit it had not occurred to me. However I realized it was the perfect time for some math lessons!! Some dates are special mathematically. Many people enjoy the sequential ones like December 13, 2015 (12/13/14). However there are other special dates. February 4, 2016 is a special one. When it is written in numbers it is 2-4-16. Can you find the relationship?

Ways to Celebrate Pi Day!

As a former math teacher, I am definitely an advocate of Pi Day which is on Wednesday this week--March 14 or 3.14. Math teachers don't always get the fun part of teaching so we have to take it whenever we can get it. Pi Day is one of those times.

For those of you who do not know anything about pi (are there people out there who do not?), pi is an irrational number (thus it is a never-ending decimal and cannot be written as a fraction accurately) that is used in math. It is one of the most well known irrational numbers and has been given the name pi after the Greek letter. It is approximated to be 3.14 or 22/7. These are usually all right approximations for most school age kids. However, you can find further approximations on your calculator or computer (see below).

There are many different things you can do to celebrate Pi Day. Of course my favorite (and most math teachers' favorite) involves pie. Yes, it is the one day we can actually have a party and justify in the math department. Always a bonus. Hazel and I will be making apple pie on Wednesday assuming we have time. I have to work out the schedule of Wednesday with Steve since he is off so we can do a grades tour at Hazel's school and we are sending Hazel to my mother-in-law's for the morning. If not we will be making pie on Tuesday and eat it on Wednesday. And or course it has to be apple pie since that is Steve's favorite dessert.

However for those of you who like to do some lessons with your children or have older children, I will provide you a few more activities. There is great reference to the number pi in history including in the Bible. There are also many different cultures that had approximations of pi in ancient times. There are several sites that have history of pi. Here are a few I found doing a google search:  exploratorium ualr      Math 4 All Think Quest. Those will at least provide you with a history of pi over the last 4000 years.

You can also find in this computer age pi calculated out to 1 million decimal places. I know some people have their students memorize pie to 100 decimal places. I'm not sure why and cannot see any reason to do this, but is an activity if you want to torture your child.

The number pi is quite simple to see how they discovered it and leads to an easy lesson for you to do with children. Your child will need to know how to divide or you will need to help them with a calculator. All you need to do is measure different circular objects. You need to measure the circumference (distance around the object) and the diameter (distance across the circle through center). pi is the circumference divided by the diameter.

Here is a Word document to do this including an additional question of plotting your answers to see the ratio.

You can also find pi by "squaring the circle". To do this you will need the vocabulary illustrated in the picture above. The radius, apothem and side length can be found in any regular polygon. As you find the area of a regular polygon with radius of one, the more sides you add the closer to pi you will get.

Here is a link to a Word document for this  activity. If you are working with a child who knows right triangle trigonometry here is a Word document with less information given.

And of course a final activity that you can do is pie charts or circle graphs. This will include reading pie charts, creating pie charts (thus knowing how to measure in degrees and knowing a circle is 360 degrees) and then doing a survey to create a pie chart. Here is a Word document to do this.

If you try any of these activities I would love to hear about it.

Mesmerizing Math -- Book Review

Disclosure: Candlewick Press gave me a copy of this book free of charge to review. All opinions in my review are my own and I did not receive any other compensation. As in all my reviews I am providing links for your ease, but receive no compensation.

Yesterday was the big math day known as Pi Day. It occurs on every March 14 since the irrational number pi is round off to be 3.14. And of course this year was even more special since if you round it off a few more digits later it is 3.1416 and thus the date 3/14/16 or March 14, 2016. Since I have already shared the Multicultural History of Pi, Activities for Pi Day and Where Pi is Taking Us in past years, I did not share any new Pi Day post. However it seems appropriate to share a fun math book this week with you. Now last week I shared a book comparing the Eastern parenting styles to the Western parenting styles and asked the question of why many Asians perform better in math and science fields than non-Asians. One of the big answers was that the Asian parents really push math at a young age. The book also discussed that the use of exploring mathematics does not work for all children and that in the Asian culture children are taught how to do the math and have it drilled in to their heads with worksheets and such. This book does not do that. In fact I would say Mesmerizing Math by Jonathan Litton and illustrated by Thomas Flintham is the perfect book that will let kids explore some of the more fun aspects of math. 

Happy Pi Day

Today is the official holiday of Pi Day!! As a former math teacher, I love to celebrate it. Last year I gave you some of the sheets I used with my high school classes to celebrate it and to justify our having pie. This year I thought I would look at a bit of the history of pi.

π  = Circumference of a circle / Diameter of the circle
A diagram of a circle, with the width labeled as diameter, and the perimeter labeled as circumference

π is the lower case Greek letter. The upper case Greek letter ∏ has a completely different mathematical meaning. π is represented by the Latin word pi, which in English is pronounced "pie." And this is where we get into the fun of π day as a math teacher and a math student. Anyway, today is π day because of its date: March 14 or 3.14.
Leonhard Euler (Source)

The earliest known use of the Greek letter, π, is in 1706 by William Jones. It was not adopted by other mathematicians until Leonhard Euler began to use it in 1736. Previously mathematicians would use letters like c or p. Since Euler had communication with many mathematicians throughout Europe the symbol took off.

The first recorded algorithm to calculate pi was around 250 BC by Archimedes. The algorithm was the main one used for over 1000 years and pi is also sometimes referred to as Archimedes constant. His algorithm is similar to one of the worksheets I developed for my geometry students here.

A painting of a man studying
Archimedes (Source)
Now based on the ratio of the Great Pyramid at Giza of it perimeter to height, some believe the ancient Egyptians had knowledge of pi. This pyramid was built in  2589–2566 BC and the ratio works out to be 2π.

The earliest written approximations for π were in Babylon and Egypt between 1900-1650 BC. In India it was recorded around 600 BC. Two books in the Hebrew Bible (written between the 8th and 3rd centuries BC) also mention use of π.

China also had approximations for π. In the beginning it was 3. Around 1 AD they had it at 3.1547. Around 265 AD, the Wei Kingdom mathematician Liu Hui created a polygon-based iterative algorithm and used it with a 3,072-sided polygon to obtain a value of π of 3.1416. he Chinese mathematician Zu Chongzhi, around 480 AD, calculated that π ≈ 355/113, using Liu Hui's algorithm applied to a 12,288-sided polygon. With a correct value for its seven first decimal digits, this value of 3.141592920... remained the most accurate approximation of π available for the next 800 years.

The development of infinite series revolutionized the calculation of  π in the 16th and 17th centuries. Although infinite series were exploited for π most notably by European mathematicians such as James Gregory and Gottfried Wilhelm Leibniz, the approach was first discovered in India sometime between 1400 and 1500 AD. The first written description of an infinite series that could be used to compute π was laid out in Sanskrit verse by Indian astronomer Nilakantha Somayaji in his Tantrasamgraha, around 1500 AD.

The discovery of calculus, by English scientist Isaac Newton and German mathematician Gottfried Wilhelm Leibniz in the 1660s, led to the development of many infinite series for approximating π. Newton himself used an arcsin series to compute a 15 digit approximation of π in 1665 or 1666, later writing "I am ashamed to tell you to how many figures I carried these computations, having no other business at the time." Throughout this time there was a lot of competition in mathematics especially in Europe including in calculating  π to more accuracy. Without going into the mathematics of it all, I will leave it at that. (However if your child thinks mathematics are boring you may want to check out the book, Mathematical Scandals, by Theoni Pappas. I always enjoyed giving my students a little side historical scandal to liven up the lesson.)

For most numerical calculations involving π, a handful of digits is sufficient. According to Jörg Arndt and Christoph Haenel, thirty-nine digits are sufficient to perform most cosmological calculations, because that is the accuracy necessary to calculate the volume of the known universe with a precision of one atom. Still people have worked very long tedious hours to calculate π to the thousands and million digits. Perhaps it is because of the human desire to beat records and the press one gets when you do with π. 

The uses of π for most people are restricted to simple geometry. Things like finding the circumference of a circle, the area of a circle, the volume of a cylinder, cone or sphere. In trigonometry, students are usually introduced to radians which involve π. (The calculation of a radian comes from using the circumference of the circle.) With further study of math, π appears in other things, but the level of math is calculus and beyond. I will share one interesting place however. 
An complex black shape on a blue background.
Mandelbrot Set (Source)

I will admit I am fascinated by fractals and have met Benoit Mandelbrot and his wife in person, so this may be why I find this one so interesting. An occurrence of π in the Mandelbrot set fractal was discovered by American David Boll in 1991. π can be computed from the Mandelbrot set, by counting the number of iterations required before point (−0.75, ε) diverges.
Me and Benoit Mandelbrot

We find further uses in physics, statistics, and engineering. Again I will not go into the mathematics and confuse many, but thought it was worth mentioning the reason why we need  π.

My source for most of this post beyond my prior knowledge as a mathematics teacher is Wikipedia.

For some other ideas on celebrating π Day visit these blogs: