Showing posts with label pi. Show all posts
Showing posts with label pi. Show all posts

March 14 - Pi Day! And Einstein's Birthday!

 Posted on March 14, 2021

This is an update of my post published on March 14, 2010:


Do you like pie?



And do you like pi?



Pi is the ratio of a circle's circumference (the distance around it) to its diameter (the distance across it).



Remember, the ratio is the same no matter how large or small the circle!


 


No matter how big or small a circle is, when you carefully measure the circumference and diameter and then divide the first by the second, you come up with the same number:

3.14159265358979323846264338327950288...



The decimal goes on a
nd on—so far, computers have computed pi out to more than two TRILLION digits! The digits never end and never repeat. Any unending, non-repeating decimal like pi is called an irrational number.

Rounding Pi


Physicists use the first 39 digits of pi, but engineers only need pi computed to 5 or 6 “significant figures” (3.1416 or 3.14
159). For most purposes, though, people round pi off to 3.14, which is why this date (3-14) is celebrated as Pi Day!




Proving Pi

1. Using non-stretchy string, carefully cut enough string to just go around a circle. This is your circumference string.

2. Now use your circumference string to measure across the circle's exact middle. Cut it. This is your first diameter string.


3. Continue to measure and cut diameter strings until you run out of circumference string
. How many diameter strings were there?

Here are more detailed instructions.

Celebrating Pi

Some years, local science museums and schools plan Pi Day celebrations. (Here is a virtual celebration.) But you can do stuff on your own, too, for sure!

Explore the Teach Pi website. Be sure to check out the Pi Day carols under the “Music” heading.

Read a poem about pi.

Look at the digits of pi. Try clicking “100,” “1,000” and so on, all the way up to a million. It's interesting to guess what, say, 100,000 digits will look like, or whether there will be a lag for the computer to load (?) or compute (?) a million digits.

Eat pie. Or have a pie-toss or pie-eating contest.



Also on this date..
.
Happy Birthday, Albert Einstein!



Albert Einstein was born on this day in 1879 in Ulm, Germany. He came to the United States in 1933 to avoid the rising
 power of the Nazis in Germany.

A theoretical physicist, Einstein is one of the most famous scientists of all time. T
he special and general theories of relativity are some of his greatest contributions; Einstein predicted the bending of light by gravity (including gravitational lensing) and contributed to the photon theory and quantum theories. He won the 1921 Nobel Prize in Physics for his work on the photoelectric effect.



Did you know...?

In 1952, Einstein was offered the position of President of Israel. He said no. (Hopefully no, thank you.)

Einstein was a member of several civil rights organizations (such as the NAACP) and defended the character of W.E.B. DuBois when he was accused of being a Communist spy.

During his life and ever after, Einstein was so famous that his name pretty much means “genius”; his face has been immortalized on everything from Beatles album covers (Sgt.. Pepper's Lonely Hearts Club Band) to Israeli money...


...he was an inspiration for Yoda's eyes (Star Wars) and for cartoons of “mad scientists” in general and "Doc" on Back to the Future in particular.





...a famous photo of Einstein sticking out his tongue was sold for more than 70 thousand dollars!

February 5 - Measurements and Records Day

Posted on February 5, 2021

This is an update of my post published on February 5, 2010:


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:

February 5, 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 was really out of whack here!

February 5, 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 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. 

That had to be a record for the most unsuccessful successful roller coaster!

February 5, 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.

Like 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 d
arned small!




February 5, 1934 – Hank Aaron was 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 have noticed that Bonds' alleged steroid use has prevented him from being elected to the National Baseball Hall of Fame, and I assume has tainted the record at least for some. 

Aaron still holds other records because of his high-level consistency over the years: he shares the record of hitting 30 or more homers in a season, for 15 seasons; he is in a tie for most All-Star games with 24; he has the most career runs batted in (2,297); he has the most career extra base hits (1,477); and he has the most career total bases (6,856). He's near the top in lots more statistical categories: 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). 

Pant, pant! 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 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. This one has roller coaster sounds and crowd response as well as music! This video includes a loop!