Showing posts with label irrational numbers. Show all posts
Showing posts with label irrational numbers. Show all posts

June 28 - Tau Day

                                                                                        Posted on June 28, 2018


Given the popularity of Pi Day on March 14 (the mathematical constant pi being 3.14), it would seem obvious that Tau Day (June 28, because the mathematical constant tau is 6.28) would also catch on.



After all, pi is the irrational number formed when the circumference of a circle is divided by diameter of that circle...





And tau is the irrational number formed when the circumference of a circle is divided by radius of that circle. 


The two mathematical constants are really similar - but we use the radius, not the diameter, in most circle descriptions and definitions. So many argue that tau is better than pi, and we should certainly celebrate it as often or more.


But...but Pi Day has all those circular pies, and everyone likes pie...and...and is there anything even remotely delicious called tau?





Hmm...


Since tau is equal to two time pi, I guess we have to have TWO pies on Tau Day! And that makes Tau Day twice as nice, am I right?


If you need more convincing, check out math YouTuber Vi Hart!

Here are a few more Tau Day memes:





You may be wondering what gives with the black-and-white circle design. This ying-yang symbol is the symbol of Taoism, which is a Chinese religion or philosophy that emphasizes living in harmony, cycles of nature, and balance between opposites. The fact that the black part of the design is a mirror image of the white part helps us to picture the importance of darkness AND light, day as well as night, ugliness alongside beauty.


The fact that the symbol of Tao is based on circles is one thing that makes Tau Day pretty rad! So, ying-yang-symbol pies?

Or some other ying-yang-based treat?







                                                                                      

Also on this date:






































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March 14 – Pi Day of the Century! (and a birthday)

Posted on March 14, 2015


I love pi (and pie), so I LOVE Pi Day. Still, I've talked about it before (most notably here - scroll down - and here), so I was thinking “been there, done that” –

BUT!

Then I realized that THIS year, Pi Day wasn't just Pi Day—it's Pi Day of the Century!

You see, pi, which is the ratio between the circumference to the diameter of a circle, is an irrational number that goes on and on and on and on...

Pi starts 3.14... (and then goes on forever, never repeating itself), and so we celebrate Pi Day on 3/14 (March 14).

But today we get this:


3.141592653 = 3/14/15 at 9:26:53 in the morning!


So get ready to celebrate Pi Minute at 9:26 A.M. today, and Pi Second at the 53-second mark!

How do you get ready? 


  • Make a Pi Day of the Century shirt.
  • Make (or buy) and eat some pie.
  • Be ready to talk about the wonders of irrational numbers that go on forever!
  • You can also join a Pi Day Facebook group!


Also, happy birthday, Akira Yoshizawa, grandmaster of origami!

Born in Japan on this date in 1911, Akira Yoshizawa is credited with raising origami from a craft to an art. He made more than 50,000 origami creations—and only a few hundred are explained with diagrams in his 18 books on origami. Most are unexplained, unique creations—although of course some people try and even succeed at copying them.

Who would even think of a self-portrait
in origami?


Origami by Brian Chan
One thing I noticed about Yoshizawa's work is that much of it is very simple. I love complicated, detailed origami, such as Brian Chan's amazing insects. But there is something so beautiful and satisfying with some of these seemingly simple pieces.

Origami by Yoshizawa
Check out a short video of Yoshizawa's work, and learn a bit of origami yourself.



Also on this date:











Physicist Albert Einstein's birthday (scroll down)

























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February 7, 2013 - “e” Day


Is it irrational to celebrate a number today?


Like “Pi Day” (March 14), “e Day” celebrates one of the most famous and useful irrational numbers. “Irrational” means “not rational,” and in math it refers to numbers that cannot be expressed as simple fractions, or ratios.

The irrational number e starts out 2.7182818284590452353602874713527...but it goes on and on without stopping or repeating a pattern. Because the first two numbers are 2 and 7, we celebrate e on 2/7, or February 7.

I bet you're wondering how on earth such a cumbersome number can be famous and useful! Well, this number is the base of the natural logarithms, and it is also used in compounding interest, which is how your bank account or other investment can increase. More money = useful!

The constant e also shows up in such places as graphs of growth or decay, the statistical bell curve, and the shape of a hanging cable or a standing arch.

(By the way, the logarithm of a number is the exponent by which the base must be raised to produce that number. Logarithms are useful in science, engineering, calculus, and computer science.)

For more about this irrational number, check out Math Is Fun.



Also on this date:
















February 5, 2010

Measurements and Records Day This is a fine day to think about all sorts of measurements and records. Don't get hung up thinking measurement is all about how many cups in a quart, or how many kilometers equals 10 miles...As for records, it's not just “longest river” and “tallest man.” Here are a few of the measurement- and record-related events that occurred today:

1897 – Measurement of circles (almost) imperiled by lawmakers! The Indiana state house unanimously passed a law decreeing that the value of pi (the ratio of a circle's circumference to its diameter) is exactly 3.2. Since pi is actually an irrational number (a decimal that doesn't end or repeat) that starts with the digits 3.141592 but then goes on and on, the value mandated by this law wasn't even terribly close. And the fact that this law was passed in the 1800s isn't any kind of excuse; a much better estimate of the value of pi has been known since ancient times. The bill never became law, luckily, because a Purdue University professor happened to be in town and coached some Indiana senators about the math involved. The bill was postponed indefinitely in the senate. The entire idea of legislating scientific or mathematical truth is what is really out of whack here!

1901 – Patent for an ellipse-shaped looping roller coaster (called “centrifugal railway”) awarded to Edwin Prescott. Called “Loop the Loop,” this roller coaster was not the first with a vertical loop, but it was the first with the ellipse shape, and therefore it was more comfortable and safer to ride. (The first two coasters with vertical loops—of the circular variety—were shut down due to accidents and injuries.) We can count this as a great success in roller coaster history! Unfortunately, more people wanted to watch it than to ride it, so much so that a viewing area was built and people were charged admission just to watch. Even with the viewing fees, Loop the Loop didn't make enough money to keep running, and it went bankrupt around the time of World War I. This has to be a record for the most unsuccessful successful roller coaster!

1915 – Richard Hofstadter born in New York City. Hofstadter went on to become a physicist; he won a Nobel prize for his work, which included “measuring” the sizes of the neutron and proton in the nuclei of atoms. Of course, these particles are really, really small: imagine taking one and a half yardsticks or meter sticks. Then cut the sticks into 1,000,000,000,000,000 pieces. That's one quadrillion (also known as one thousand million million) pieces. That's...well, pretty darned small!

1934 – Hank Aaron born in Mobile, Alabama. Aaron grew up to be one of the greatest baseball players of all time. He played from 1954 to 1976, and he held the Major League Baseball (MLB) record for most career home runs, with 755 homers, for 33 years. Even now that his record has been broken by Barry Bonds, I can't help wondering if Bonds' alleged steroid use may invalidate the new record. Aaron holds other records because of his high-level consistency over the years: he had 24 or more home runs every single year from 1955 through 1973; he's the only player to hit 30 or more homers in a season at least 15 times; he made the All-Star team every year from 1955 to 1975; he has the most career runs batted in (2,297); he has the most career extra base hits (1,477); he has the most career total bases (6,856); he's in the top 4 of seasons with 150 or more hits; he's third in career hits (3,771); he's tied for fourth (with Babe Ruth) in with career runs (2,174); he's second in at-bats (12,364); he's third in games played (3,298). There are an awful lot of numbers in baseball—and these don't even involve averaging!

Measuring Everything in the Universe

New Grounds has an interesting “interactive diagram” about the size of things. When you first enter, you can see the size of things at a human scale, such as an adult human (1.7) meters, giant earthworm (an amazing 7 meters!), and a large beach ball (1 meter). Slide the little slider button to the right, and you can see huger and huger objects, including planets, starts, and galaxies. Slide the button to the left, and you can see tinier and tinier objects—going down to atoms, protons, and even to the as-yet undetected “strings” that may make up quarks.

It's Rational to Like Irrational Numbers
There are some pretty fun books about numbers. Have you read Math Curse, by Jon Scieszka? How Much is a Million? by David M. Schwartz and Steven Kellogg?

For older readers, how about A Gebra Named Al, by Wendy Isdell? I haven't read it, but Sir Cumference and the Dragon of Pi, by Cindy Neuschwander, sounds really fun! (This author has a whole slew of math storybooks!)


Take a Virtual Roller Coaster Ride!
This one has several loops and realistic coaster sounds. This one has no loops and is set to music. It's pretty extreme and made me feel like I was really moving for a second or two.