New YouTube Series: Musimathics!

Finally the release of Musimathics is here!! Integrating both music and math he series is written and explained by Center of Math employee, Chloe Weiers, a co-op student studying Music and Mathematics in Boston.

Musimathics covers a broad range of topics from the field of mathematical music theory. Each video gives an overview of a topic or range of topics from this broad field of study. The series covers everything from geometric modeling to Fourier analysis and fractals. Each lighthearted video contains musical examples and explanations of the relevance of those examples. This series implores you to change the way you listen to and experience music, without ever going over your head with complicated mathematics. Even if you don't have a broad background in mathematics, you will be able to appreciate the beauty of the mathematical nature of music presented in this series!

After sitting down with Chloe we asked her what was her inspiration was behind combining these two intricate subjects together. Her answer is as follows:

"Well, this past academic year I have been working on early research on applications of dynamical systems theory to music. Many of the topics I have explored in my research stem from very simple, yet interesting concepts from mathematical music theory. I thought it would be cool to bring some of these ideas to our audience here at the Center of Math. Thinking mathematically about music, or any art, really, provides fresh perspective and new ways to listen. My goal with this series was to pique interest in the subject, not necessarily to give any in-depth explanations. With this broader outlook, you can better appreciate the landscape of the subject."

Feel free to comment with any questions or thoughts you may have, we hope you enjoy it! 

Advanced Knowledge Problem of the Week

See what you can come up with for this week's Advanced Knowledge Problem of the Week!

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Fun Friday: World Tesselation Day

"The geometry of space translates to a reoccurring theme in my creations: the tessellation." - M.C Escher

M.C Fisher was one of the artists responsible for leading the art of tessellation. Today, June 17th, is M.C Escher's birthday. This served as the inspiration for Emily Grosvenor's push to create World Tessellation Day. Grosvenor is the author of a children's book about a girl named Tessa who sees patterns everywhere titled, Tessalation. 

What is a tessellation?

Wikipedia

According to Escher, a tessellation is an arrangement of closed shapes that completely covers the plane without overlapping or leaving gaps. In mathematics, tessellations are broken down farther through descriptions. A tessellation with a repeating pattern is periodic, while a non-repeating pattern is called non-periodic. An edge to edge tiling is a polygonal tessellation where adjacent tiles only share one full side. The sides of the polygons and the edges of the tiles are one in the same. A monohedral tessellation contains tiles that are all congruent. The Hirschhorn tiling uses all irregular pentagons. There are many other types of tessellations whose labels are dependent on color, vertices, edges, shapes, or levels of symmetry. Tessellations can also be raised to a higher dimension.  For a complete list of tessellations, check out this Wikipedia Page.

Where can you find tessellations?

Roman mosaic, Wikipedia

In simple terms, everywhere! Tessellations can be created as art, through manufacturing, or in nature. 

Art: Tessellations are often featured in quilts, woven or stitched. In Ancient Rome and Islamic art, tessellations were used to decorate temples and as decorative pieces in buildings. M. C Escher was inspired by Spanish and Moorish symmetry on a visit in 1936. Tessellations are not limited to any particular mediums, and can be found in any genre of art. 

Manufacturing: Tessellations are often used in manufacturing to reduce waste. An example of this is found in sheet metal, when the cutouts for various products are engraved and later cut out. Many products are also designed with tessellations. This is evident in the bottom of a Vans sneaker, certain chain link fences, or as designs on household goods. 

Honeycomb

Nature: While some tessellations are created by man, some are found naturally. The most common example is a honeycomb, which is filled with hexagons. Tessellation patterns can also take the shape of a checkered pattern, found in trees or certain flowers. Gilbert tessellations are random crack networks, that form non-periodic functions in nature. 

How do you celebrate World Tessellation Day!?

Image by: Pedrita

This is an easy one. You can celebrate by creating a tessellation! This can be as a doodle, an art project, or a math problem! Check out this Tessellation Tutorial. You could also read up on M.C Escher, or read Tessalation, which comes out today! Be on the look out for tessellation products, such as these cool water bottles! 

Problem of the Week

This week's Problem of the Week asks you to derive an expression for the quotient of two twice-differentiable functions. Let us know how you do in the comments!

Solution below the break.

Advanced Knowledge Problem of the Week

Don't miss this week's Advanced Knowledge Problem of the Week!

Solution below the break.