CAMP 2021 Day 3 – Half Way Through

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Pin-Shan Lai
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Welcome to CAMP Day 3! CAMPers had worked their way through the week with hard work and creativity. Today’s work focus on the application of tessellations. Each class explores topics on tessellations with CAMPers experimenting with each subject with their hands.

 

In Shuang‘s Art Class, CAMPers begins with exploring different real-life tessellations. For instance, bee comb, turtle’s shell, pineapple, and tiles.

CAMPers working on real-life examples with tessellations

 

CAMPers later have a conversation on “Why does tessellation exists?” They give out several reasons: natural efficiency, saving space, and having an arch-like shape like a turtle shell to provide protection. 

CAMPers are also introduced to Voronoi Tessellation. Unlike the tessellations CAMPers encountered before, Voronoi Tessellation spreads out in a less equal pattern yet still having connections on a plane. For instance, a giraffe’s skin will be a Voronoi Tessellation.

To make the objective clear, CAMPers play a supermarket imagination activity that Shuang designed. This activity involves CAMPers imagining themselves in a supermarket and making various points outward.

 

Voronoi Tessellation is different from the tessellation CAMPers discussed

 

CAMPers later designed their own chicken pattern through origami papers. Chicken patterns design is also used in this year’s CAMP T-shirt (by Shuang!).

CAMPers made their own chicken shape design
CAMPer working on the self-created tessellation book

In Grace‘s Art Class, CAMPers also work on chicken patterns making. CAMPers also learn how to fold chicken pattern from scratch and to construct several chicken patterns together to form a tessellation.

Chicken Pattern Tessellation

 

CAMPers also learn how to make their own tessellations through reconstructing and connecting each pieces together.

CAMPers learn how to make their own tessellation

 

In Karen‘s Computer Science Class, CAMPers write codes to form images. They then translate the images they create and create the shape over and over again. Eventually, they make multiple shapes that form tessellations. 

 

CAMPers write codes on translating the image they create
By Rotating shapes, CAMPers create different patterns
The final product – tessellation!
CAMPer’s tessellation work
CAMPer in Karen’s class working with tessellation codes

 

In Frances‘s Math Class, CAMPers in SINE and COSINE are figuring out how to find the sum of the angles of a polygon using the fact that each triangle’s angles sum to 180 degrees.

CAMPers working on degrees in polygons
CAMPers learn how to divide polygons into triangles

Unlike going straight to definition, CAMPers have their hands on experience on testing out different angles to see how different polygons work. After these observations, CAMPers calculate what each angles are and label out each angles of the polygons.

In addition, CAMPers in secant and cosecant have figured out
       1) The number of degrees in each angle of a regular polygon
       2) That each vertex of a tessellation must be surrounded by polygons whose angles add to 360 degrees
Next they began to make use of the rules to create tessellations with more than one shape of polygon.
In Japheth‘s Math Class, CAMPers work on solving polygon tessellation around a point problem. CAMPers are introduce to both geometry and algebraic ways to understand tessellations.
Ways of understanding the polygon tessellation around a point problem

As we get to the middle of CAMP, CAMPers continue to show effort and passion in the topic being introduced. Through activities and experiment, math becomes a fun activity and knowledge for all!

 

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Japheth Wood

I’m Japheth Wood (he/him), the Bard Math CAMP co-director, and a math professor at Bard College. CAMP (which is an acronym for Creative and Analytical Math Program) is a very special week of the year for our young math community. It's inspiring to see our students return year after year. This is our 11th summer of CAMP! We're back once again on the idyllic Bard College campus in Annandale-on-Hudson, and thankful to the CAMP students, parents, and staff, for making this mathemagical week happen. Notably, we've (finally) had our first CAMP reunion this past June, an event that I know will grow to be an integral part of what we do.

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Frances Stern

My name is Frances Stern (she/her/hers)! I’ve been teaching math at CAMP since the first year, making sure our math theme has a connection to art and computer. It’s fun to show students math that they don’t see in school. I've retired from daily teaching but continue to teach for the New York Math Circle & students who are seeking more math in their lives. My hobbies include learning to draw, paint, & juggle, reading, walking & folk dancing. I’ve written 2 books for teachers and parents called “Adding Math, Subtracting Tension” (for different age-ranges of children). They pay as much attention to how to keep out of a fight (what many parents told me is a problem) as they do to math.

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