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Thursday, April 30, 2015

Throwback Fact: Gauss's Birthday

Carl Friedrich Gauss
On this day in 1777, Carl Friedrich Gauss was born. The Prince of Mathematics was an important part of our Math Madness competition, and made it to the Final Four round. But in his short bio on our webpage, we missed some facts about Gauss that make his life even more interesting and impressive.

The great mathematician would have been 238 years old today, but there was a time that he did not know the date of his birth. Gauss was born to poor, working-class parents, and his mother was not quite literate. She did not record the date of Gauss's birth. Years later, she could just recall that Gauss was born on a Wednesday, and it was 8 days before Ascension Day, which lies on the calendar 40 days after Easter Sunday.

Tuesday, April 28, 2015

8 Vacation Destinations for the Mathematician

It’s been a long, hard Winter for the Center of Math. From record snowfall totals to Spring days that just can’t make it to feeling “warm,” we’ve got cabin fever and we’re craving Summer. So we put together this list of our top eight vacation destinations for mathematicians.

Westminster Abbey
London, England: If you’re in the UK, you know there’s a lot of math history around you. We suggest a visit to Westminster Abbey, where you can see the final resting place of Sir Isaac Newton, one of the greatest mathematicians and scientists of all time. If you’re able to venture a bit outside of the city, go to visit Bletchley Park. This museum is located at the site of the Government Code and Cypher School where Allied forces worked to decipher military codes of the German, Japanese, and other Axis nations. The codebreakers working here, including Alan Turing, created the technology that made modern computers possible.

Monday, April 27, 2015

Problem of the Week

That weekend was too short, wasn't it? But anyways, we're back at the Center with a new Problem of the Week. I've been feeling logic problems more and more since Cheryl's Birthday a few weeks ago. I particularly like the problems that lean more mathematical. The problem below, which I posted on our Facebook, Twitter, and Google+ accounts, looks so short and simple compared to some past problems of the week. But looks can be decieving! I found this problem on this Reddit comment. The user posted a quick solution in a follow-up comment,but I've expanded it and made it more detailed below.
Click on any picture to expand!
This problem can be solved using simple mathematics. In theory, a young high schooler has all of the math skills required to solve the problem, but it requires a few very logical steps. Here's my solution:

Friday, April 24, 2015

Math Minds: Scott Kelley

Last weekend, the Center of Math team went to the NCTM conference held in Boston. At the conference, we met hundreds of math teachers from the United States and abroad (the first person to stop by our booth was visiting from Perth, Australia!), and one of our interns, Zach, jumped at the opportunity to interview a few of the visitors. 

Here's his interview with Scott Kelley, a math instructor at the Texas School for the Blind and Visually Impaired. Read on to find out about how the blind "see" math problems, how his students use technology, and what simple advice Mr. Kelley offers to all students...

Zach talking math with Scott Kelley at NCTM

Thursday, April 23, 2015

Throwback Fact: The AMS

An image from our Instagram, when the Center
attended JMM (by the AMS) in January
Friday, April 24th (misaligned slightly from our Throwback Thursday) marks the 118th anniversary of the first sectional meeting of the American Mathematical Society in 1897. Founded nine years previously in 1888, the AMS was the result of Thomas Fiske's vision to create a version of the London Mathematical Society in his home country. Soon after being founded, the AMS began to publish a research journal periodically.

Today, the AMS has nearly 30,000 individual members across the country, with physical locations in Providence, Rhode Island, Ann Arbor, Michigan, and Washington, D.C. And the AMS works today, like in the earliest days of the society, to publish math content- they've upped their postings from one research journal to 8(!), plus 4 translations journals, and two open source journals. The AMS is a wealth of mathematical knowledge.

The AMS works each year with the Mathematical Association of America (MAA) to put on the annual Joint Mathematics Meeting. In fact, the Center of Mathematics regularly attends- we were at JMM San Antonio this past January!

To read more about the American Mathematical Society, click here or visit their webpage.

Wednesday, April 22, 2015

Math and the Earth (and a Giveaway!)

Math intern Tori and two friends in Center of Math wristbands out in nature.
Find out how to get your own at the bottom of the post!
In the Center of Math's 100th blog post, let's talk about Monther Earth. 

Math and nature go together. Despite the math quote of the week that we posted last Sunday, I think that math is not a construct of the human mind- it’s always existed and it always will. This is evidenced all over. Sunflower seeds are arranged on the flower in a golden spiral, the ratio between your forearm and hand is the Golden Ratio, objects fall to Earth at (ignoring air resistance) an exponential rate, and the fractal patterns found on Romanesco broccoli (pictured below with a sunflower) are mesmerizing. In fact, the universe may even be made of math.

Monday, April 20, 2015

Problem of the Week: Marathon Monday Edition

Happy Marathon Monday to all of our followers! It’s been a busy weekend for the Center of Math. We had a very successful couple of days at the NCTM 2015 conference! It was three days packed full of math people, thanks to each and every one of you for stopping by to chat with us. And since Friday afternoon, Boston has been buzzing with tourists, runners, and locals alike as everyone gets pumped for the marathon. In fact, I might have to alter my route home after work depending on when the runners finish.

For today’s Problem of the Week, which I posted on our Facebook, Twitter, and Google+ as usual,   I wanted to do a marathon theme. I created the problem below, which I adapted from this Washington Post blog.  

And as always, Monday comes with my messy handwriting providing the solution below...

Thursday, April 16, 2015

Throwback Fact: Leonardo Da Vinci

Da Vinci self portrait
Choosing just one topic for a throwback was difficult this week. On this day in 1705, Isaac Newton was knighted by Queen Anne at Trinity College. If you'd like to read a little more on Newton, a past intern did a throwback fact on him here. And Wednesday, April 15th marked two anniversaries- the birth of our Math Madness Champion Leonhard Euler in 1707, and the birth of Leonardo Da Vinci in 1452. 

While he is definitely not a mathematician, Leonardo Da Vinci was a polymath, and contributed many quality works in his lifetime that interest mathematicians today. The original renaissance man, Da Vinci was a master in many areas. His paintings are likely to remain famous for all of human history, and his notebooks fascinate scientists to this day- he worked with codes, he fantasized about flying machines, sketched human anatomy, and much more.

Tuesday, April 14, 2015

Are You Smarter than a Singaporean Math Olympiad Student?

The original problem, as seen on Facebook
We follow as many math sites as we can keep up with here at the Center of Math. So when this image began circling the internet yesterday, we were intrigued. I tried working the problem when I got back to the office from lunch yesterday (kinda half-heartedly, I admit) and thought through the logic, and originally got the problem wrong. My logic was there for a step or two, but I didn’t take it far enough.

I didn’t like the explanations I found on various sites early yesterday afternoon, so I decided to write up my own and post it here for the Center of Math followers.
I wrote the dates this way- it makes it easier to see them laid out like this
First, Albert says something along the lines of “I don’t know the answer, but I do know that Bernard also doesn’t have the answer.”

Monday, April 13, 2015

Problem of the Week

Happy Monday from the Center of Math! It's finally spring where we are- it was such a nice weekend and we were reluctant to let go of the weekend. Monday means Problem of the Week, and I've got it right here:
I posted the picture above to each of our social media outlets, and I've posted my solution below...

Thursday, April 9, 2015

Throwback Fact: Knot Theory

A trefoil knot, the most simple non-trivial knot
According to The Math Book by Clifford A. Pickover, "The use of knots may predate modern humans (Homo sapiens). This statement is absolutely fascinating, and prompted a research session on a portion of mathematics that the Center's math intern hadn't encountered yet.

A mathematical knot is different from what people normally think of as knots. Instead of a piece of string with two free ends and a tangle in the middle, mathematical knots come from embedding the unit circle into three dimensions, and twisting and disturbing the continuous line from there. Almost always, knot theorists are studying closed loops. From this point, it's important to note that a knot can be trivial (also known as an unknot), and in this case the loop can be unfurled to be a single unit circle loop. For a knot to be non-trivial, it will always have crossings no matter how the "string" is pulled.

Tuesday, April 7, 2015

The Center and the Community

Zach from the Center of Math helps Juan from Boston Latin Academy load the books. 
Today, April 7th 2015, the Worldwide Center of Mathematics completed a good deed, and helped over 170 students all over Boston get the tools they need to be the best students they can be. With some help from Esther Kan, a librarian at the Campbell Resource Center in Dorchester (a division of the Boston Public School system), employees at the Center helped give textbooks to high school students who needed them.

Because we’re so excited about this whole experience, we’re going to break down the specifics a bit more. The Center of Math had 25 copies of Introduction to Statistics, 36 copies of Worldwide Pre-Calculus, and nearly 125 (!) copies of AP Calculus to donate to various schools.

Boston Latin Academy received 80 copies of AP Calculus, Madison Park High School and East Boston High School split the 25 copies of Intro to Stats, English High School received 21 copies of AP Calc, and Brighton High received the last 25 copies of AP Calc. All of the schools will split the Pre-Calc books amongst themselves.

The lack of textbooks perfectly represents the inequality that is too prevalent in America’s public school systems, and is one of the main reasons that the education and income gap continue to grow in the U.S. One of the beliefs that motivates the employees at the Center of Math is the idea that education should be available to anyone who wants to learn. This idea is why our textbooks are so affordably priced, and this is why our YouTube channel is stocked with informative videos and lectures – if you want to learn, we are here to help.

We are thrilled to have played such an integral role in making so many students’ education easier, as well as lightening the stress-load that these teachers had been dealing with. We know that these students will use the books in good health and with good intentions. The idea that we may have sparked one student’s passion for mathematics is enough for us, but knowing that these kids now have the textbooks they need, well it is a great feeling and it has motivated us to try our hardest and do more good in the education world. 

Math Madness Results

Click to expand the image!
The Madness has ended!!

In the last Math Madness blog post, we released the winners of the Elite 8 matchups. Then we were down to the Final Four: Newton was up against Gauss, and Euler had to face Riemann. We set up a poll on Friday night and our voters decided: Newton won his match, and Euler his. So we entered the championship last night.

So the two mathematical giants faced off, and we set up a new poll on Monday night to ask our voters to help us decide the winner, the most significant mathematician of all time, and the result is...

Monday, April 6, 2015

Problem of the Week

Good morning from Cambridge! I hope everyone had a great Easter weekend- I spent mine cooking brunch. Now that everyone is back to work, take a short break and solve our Problem of the Week. Like usual, I posted a challenge problem to our Facebook, Twitter, and Google+ pages, and it can be found right here:
Click to make the picture larger!
A proof! This one doesn't look too tricky. I've uploaded my solution (hint: use modular numbers!), and it can be found below...

Thursday, April 2, 2015

Math Madness: The Elite 8

As we whittle down our list of mathematicians, the choices get harder and harder. We published all of the results of the Sweet 16 (click the Math Madness label in the sidebar if you need to find an old post!) and we've got the Elite 8 results right here.

Match 1: Newton vs. Erdös

Check out these short bios for Newton and Erdös.

Both men were important, and both men had eccentric personalities according to biographies. Erdös was a self-proclaimed “solver” more than an innovator of mathematics. For this reason, we award this round to Newton, who created calculus, an entire branch in the tree of mathematics, as well as solving problems of his time. But, Newton will never have a good Erdös number!

Throwback Fact: President Garfield, Mathematician?

President James Garfield
Several weeks ago, the Throwback Fact of the week focused on the Pythagorean Theorem. But did you know that the United States has a past president with a published work of mathematics? On April 1st, 1876 (yesterday in history!) James A. Garfield, a congressman at the time, published a unique proof of the Pythagorean Theorem in the New England Journal of Education. 

Wednesday, April 1, 2015

Math Madness: Round 1 Part 4

Here is the final update on the matches of our Sweet 16 in the Math Madness Bracket! Keep checking both the blog and the website for updates. One more blog post will show the results of our Elite Eight matches, and then voting will be open to all Center of Math readers to decide our Final Two and then the Champion!

Match 7: Hilbert vs. Poincaré

Click to make the image larger!
Match 7  shows two mathematicians from the same era against each other: the German David Hilbert versus the French Henri Poincaré.

A mathematician who got his feet wet in many branches of mathematics, Poincaré has earned credit for the creation of generalized elliptic functions, the discovery of connections between automorphic functions in the same group, the Poincaré conjecture, and much more. Perhaps his most prestigious contribution was the solution of the three-body problem, which eluded mathematicians since Newton. Poincaré had a strange path to mathematics- he actually earned a degree in mining engineering, and became a mine inspector for several years. He was actually completing his thesis for a mathematics doctorate at the same time in the field of differential equations. In 1912, Poincaré died at the age of 58.