How to Have a Math Filled Summer

Summer of Math

Summer is a time for warm weather and relaxation, but it doesn't mean education has to come to a grinding halt. Learning and increasing your knowledge comes in many different forms, and we created the #EverydayMath series to prove this! So far, we have outlined ways that mathematics can be present in books, movies, television shows, or games. The summer is a great time to explore these areas, where math can intersect with other academic categories. To jumpstart your summer plans, we will recap these posts and include new ideas that can help to fill the coming months with educationally enriching activities!

Many people use the Summer as a time to get away. Whether it's a few days or just a few hours, here are some attractions that will appeal to all math enthusiasts!

Math Attractions

1. National Museum of Mathematics

Museum Website

Twitter: @MoMath1

    The National Museum of Mathematics is a great place for any math lover to visit. Located in New York City, the museum features a number of interactive exhibits, a gallery of mathematical structures, pictures and art, as well as programs that explore the wonders of mathematics. This is the place to be for anyone who wants to spend a day of fun, immersed in a world of mathematics. 

2. MIT Museum

Museum Website

Twitter: @MITMuseum

     Right in our backyard (Cambridge, MA), MIT is a center of math and sciences. The MIT museum is meant to engage and inspire visitors about the possibilities and opportunities science and technology have to offer. The museum features interactive exhibits, public programs, and its own world-renown collections. Any math lover should visit the museum and see one of the most influential mathematical places in the world.

3. The Tech Museum of Innovation

Museum Website

Twitter: @TheTechMuseum

     Located in San Jose, in the the heart of Silicon Valley, the Tech Museum of Innovation is a great place for any math lover to visit. The museum features many different programs and exhibits designed around tech innovation. One such exhibit involves designing and building your own robot! This is a great place to see what the latest innovations in technology are, all involving math of some kind.

Here are ways to stay in your own backyard, but still put a math twist on your summer!

Everyday Math: Books

April 29, 2016

Imagine this combination: a comfortable beach chair, beautiful weather, and a good book. It's difficult to imagine anything that may top that, but what if that book was a math book? 
Here are 3 top selling books about mathematics.



Fermat's Enigma
by Simon Singh
1997

This National Bestseller is not a biography of Fermat or an explanation of his theorem, as the title might suggest. Instead, Singh delves into the lives of people who dedicated their time and careers to proving Fermat's Last Theorem. The book creates a more personalized view of mathematicians. The heartbreak, mastery, and critical moments of these great minds are documented in a way that humanizes the subject.


Zero: The Biography of a Dangerous Idea
Charles Seife
2000


This non-fiction book examines the idea of 0 and explains the controversiality surrounding the number at some points in history. It traces back to the Babylonian roots of 0 and takes a look at "one of the great paradoxes of human thinking". He writes the topic in a thrilling and interesting way, receiving great reviews from the Mathematical Association of America.


The Drunkard's Walk: How Randomness Rules Our Lives
Leonard Mlodinow
2009

This choice is not as firmly rooted in mathematics as some others on this list, however it is still a great read that combines probability, statistics, and how they impact society. Mlodinow demonstrates how our lives are strongly determined by chance, even when there seems to be a clear system set in place. Ranging from political polls to corporate success, his examples are compelling and interesting. By combining psychology and statistics, The Drunkard's Walk takes an applicable approach to mathematics.


Everyday Math: Math Games and Logic Puzzles
April 1, 2016

Maybe you prefer keeping your mind on tract with puzzles or logic games. Here are some Sudoku alternatives that will keep you thinking!

Calcudoku

Similar to Sudoku and Killer Sudoku, Calcudoku follows the same basic directions. Instead of having to fill in the numbers according to sums, like in Killer Sudoku, Calcudoku provides a number and a certain mathematical operation. The numbers in the smaller boxes must compute to the number given, using the function noted. Again, no numbers are filled in before you begin, so the mathematical functions are the only hint you have! If you enjoy mental math, this is probably the twist on Sudoku you would enjoy the most! Below is an example with some numbers already filled in.


Bongard Problem

Bongard problems differ from the previously mentioned Sudoku puzzles. Have you ever played spot the difference in a children's magazine or book? Well Russian Scientist M.M Bogart created a similar game in 1967. Bongard problems are based on visual pattern recognition. There are 6 shapes or figures on the left, and six figures on the right. The six shapes on the left all share a common characteristic with each other or follow the same rule. The shapes on the right also share a common trait with each other, but something separates them from the shapes on the left. The game is to figure out what the difference is between the two sides. In other words, it's your job to find the rule that each side follows or does not follow. Check out the example below, a medium level problem.


Everyday Math: Math in the Movies
March 11, 2016

Even the Summer has its rainy days, and sometimes it can be nice to spend a day inside. Don't worry! This can be a great excuse to watch a movie centered on mathematics!

The Story of An Underdog: Good Will Hunting

Known as a classic math movie, Good Will Hunting is a must-see. This underdog tale has a romantic twist and stars both Matt Damon and Robin Williams. Matt Damon's character, Will Hunting is a troubled young adult who's life path weaved in and out of foster homes and trouble with the law. While working as a janitor at MIT, he is able to solve two math problems that were created for graduate students. A professor at MIT took interest in Will, noticing his affinity towards mathematics and genius-level ability. Along his journey, Will faces his inner struggles with the help of a therapist (Robin Williams), and meets a romantic interest who helps to shape his life. The math problem that Will faces on the board is actually a real problem, although not as difficult as it is made out to be. The problem involves a feature of graph theory, homeomorphically irreducible trees. Pictured below is the problem that sent Will into the realm of academia. Interestingly enough, the math brains behind the movie actually appeared on screen as well. Patrick O'Donnell, who had a minor roll in the bar scene, actually ran the math department at University of Toronto at the time. O'Donnell and John Mighton, who plays the professor's assistant, chose the equations and theorems used in the movie. 

The Classic: A Beautiful Mind
A Beautiful Mind is based loosely on the real life story of John Nash, a Nobel Prize winner. Russell Crowe plays John Nash, a mathematical genius that specialized in game theory, differential geometry, and differential equations. Game theory can be utilized in fields such as economics and political science. In fact, Nash won his Nobel Prize in economics. In a famous scene, the film dramatizes Nash's discovery of the Nash equilibrium, a term used in economics and game theory. The film is said to take artistic interpretation of Nash's real life, but the mathematics in the movie are based on real theorems and theories. The director of A Beautiful Mind enlisted the help of a mathematics consultant, Dave Bayer of Columbia University, to ensure the mathematics were correct throughout the film. The movie contains some math jokes and facts that may only be clear to those well versed in mathematics. For an example, at the end of the film, a student wants to show Nash a proof exploring the idea that "finite Galois extensions are the same as covering spaces", which is actually a true statement. Along with his prowess in mathematics, A Beautiful Mind also demonstrates Nash's story of mental illness and schizophrenia. His schizophrenia initially impacts his career, but he is able to recover and take his place as one of the leading mathematical and economic minds of his time.

Everyday Math: Games and Logic Puzzles

Everyday Math: Math Games and Logic Puzzles

It is easy to recognize the benefits of physical exercise– muscles can grow, a number on a scale can shrink, and progress is measurable. However, there is another type of exercise that goes unrecognized. Although the brain is not a muscle, 'exercising' this organ can reap huge educational benefits. Studies show that stimulating your brain can help improve brain activity and help to prevent deterioration as the brain ages. Scientists say that the brain, like a muscle, can be trained to improve memory and problem solving. Now, you may be thinking, "Great, more homework...",  but using your brain doesn't have to be a mundane task. Infusing your day with some logic puzzles and games is a great way to both exercise your brain and add a little more math into your daily routine. Check out our favorites in this post. Challenge yourself to pick up a puzzle book instead of scrolling through your newsfeed during your down time!

Sudoku

We'll start with an easy one. Sudoku ranges in difficulty levels but this classic puzzle is probably the most common. Sudoku forms the basis for several other puzzle-type math and logic games.

A Sudoku board is pictured above. The grid is broken down into boxes, rows, and columns. There are also some numbers already filled in. The objective of the puzzle is to label each of the small boxes with a number 1-9. Doesn't sound too bad, right? The tricky part is that 1 number can't appear twice in a row, column, or box. In other words, each box must have one of each number (1-9). The same is true for the rows, as well as the columns. If one number is out of place, you may have to rearrange your entire board. Math may not be directly related, but the same problem solving capabilities and reason required for thinking through math problems will help you in Sudoku! Sharpen your pencil, because this is definitely not something to complete in pen!

Killer Sudoku

Don't let the name fool you! Killer Sudoku is just like Sudoku but with an added challenge. The game still follows the same rules as Sudoku– with one added twist. On the board below you will see dotted lines outlining various shapes. Some only have 2 boxes, while some have up to 7. You will also see small numbers inside those dotted boxes. These numbers represent the sum of the numbers within the dotted lines. Unlike regular Sudoku, there are no numbers already filled in for you, so your only hints are the sums. The higher level Killer Sudoku puzzles have higher numbers as the sums, creating more possible number combinations. Give it a try!

Calcudoku

Similar to Sudoku and Killer Sudoku, Calcudoku follows the same basic directions. Instead of having to fill in the numbers according to sums, like in Killer Sudoku, Calcudoku provides a number and a certain mathematical operation. The numbers in the smaller boxes must compute to the number given, using the function noted. Again, no numbers are filled in before you begin, so the mathematical functions are the only hint you have! If you enjoy mental math, this is probably the twist on Sudoku you would enjoy the most! Below is an example with some numbers already filled in.

Bongard Problem

Bongard problems differ from the previously mentioned Sudoku puzzles. Have you ever played spot the difference in a children's magazine or book? Well Russian Scientist M.M Bogart created a similar game in 1967. Bongard problems are based on visual pattern recognition. There are 6 shapes or figures on the left, and six figures on the right. The six shapes on the left all share a common characteristic with each other or follow the same rule. The shapes on the right also share a common trait with each other, but something separates them from the shapes on the left. The game is to figure out what the difference is between the two sides. In other words, it's your job to find the rule that each side follows or does not follow. Check out the example below, a medium level problem.

Solution: The shapes on the left are convex, while the shapes on the right are concave.

HyperRogue and hyperbolic geometry

One mathematical field that I find particularly interesting and beautiful is hyperbolic geometry: it's the same as Euclidean geometry, but takes the axiom that for any line and any point outside of that line, there's more than one line passing through that point which doesn't intersect the given line. In the past, hyperbolic geometry has featured heavily in the works of mathematically inclined artists like M.C. Escher.

Recently, over the past few years, independent developer ZenoRogue has created a video game that utilizes hyperbolic geometry, by the name of HyperRogue. The game is in the roguelike genre, but rather than using turn-based game evolution on a square or hexagonal grid, the game is based on the truncated order-7 triangular tiling of the hyperbolic plane, often called the "hyperbolic soccer ball," which is what gives it all sorts of interesting non-Euclidean properties. Keep reading to watch a Center of Math original video of HyperRogue gameplay, along with commentary about how the mathematical properties of hyperbolic space affect the game.

Holiday Math: Dreidel Simulation

Happy Hanukkah, Center of Math fans! Since today's the first day (in Cambridge) of the holiday, I decided to take a mathematical/computational look at the dreidel game, one of the many traditions practiced on Hanukkah. Keep reading to learn how the game is played, and to see what I found out with my simulation of the game—the results may surprise you!

Throwback Fact: Mancala

An example of a modern Mancala board from Europe
Source: https://en.wikipedia.org/wiki/File:Bao_europe.jpg

        Many historians believe that Mancala is the oldest board game in existence. Since Mancala is one of our favorite games in the office we decided that for the throwback fact of the week we would take a look at Mancala.

        Mancala is a/the term used to describe a collection of similar games, of which there are over 800 around the world. Some of the variations include Bao, which is played across the east coast of Africa, Oware, which is played in the Caribbean, and Kalah, which is the modern game played in the US and Europe, which we call Mancala. It is unclear exactly where Mancala originated but many historians believe it was in Africa where players used to carve holes in the ground and use pebbles to play.

Bao players in Zanzibar 
Source: https://en.wikipedia.org/wiki/File:Bao_players_in_stone_town_zanzibar.jpg

        There are many different theories as to what the original purpose of the game was for ancient people. One theory is that it was a record keeping system used to manage debit and credits, which were represented by the two sides of the board. Another theory is that Mancala was a ritual at funerals, weddings and other ceremonies. It could also have just originated as a game, which is its main use now.

        Whatever the origins of Mancala one thing is for sure, ancient people needed to count to play, just like we do now. Mancala is a great game for teaching kids how to count and work on strategic thinking skills as they age. 

Tell us, what are some of your favorite board games?

Source: 1, 2, 3