CAMP 2021 Day 5 – Time to Say Goodbye

We cannot believe it is CAMP Day 5 already! Welcome, all staff, parents, and CAMPers to Day 5. Today, before we head off to a new journey, we would like to introduce our CAMP 2021 Photo Gallery on the main page:

Bard Math CAMP More Information

If you clicked into every small circle (Yes! Math Circles!), you will realize there are a larger photo AND small descriptions of each photo. These photos start from Day 1 to Day 5 and are kindly given to us by CAMPers, parents, and staff. 

We begin Day 5 with Karen‘s Computer Science class. Today, CAMPers are to build their own 3D model based off on the codes they write on Tinkercad.

CAMPers first went back to their codes to set off the background to be transparent to transform into a 3D model. Then, Karen introduces Tinkercad to CAMPers and they try it out themselves!

Although it is a new programming website, CAMPers are never afraid of trying out new ideas.

CAMPers start off from the original programming and changing the background into transparent like.
CAMPers are to make their borders clear for the model. The model can later be used for laser cut or 3D printing.


In Japheth‘s Math Class, CAMPers went through the history of tiles and tessellations. It begins with several mathematicians’ discoveries of the different tile sequences. Through different polygons, mathematicians discover several possible sequences. There are several types ranging with different combinations of polygons that built up to this research.

Over decades, mathematicians are finally able to come with a closer explanation of tessellations. While many remain found, there are still undiscovered patterns.

One famous mathematician, Martin Gardner, dives into the research of interesting graphics. This later becomes the turning point of tessellation discovery.

In Frances‘s Math Class, Sine and cosine students figured out that the sum of the degrees in the angles of a polygon can be found by multiplying 2 less than the number of angles by 180, (n – 2) x 180.

Although some had been told the formula, they were able to see why this formula works. All students worked to find more semi-regular tessellations, figuring out many of them and also making tessellations that they realized are not semi-regular, but quite pretty. Hope CAMPers can go back and share what these all are!

In Anish‘s Computer Science class, CAMPers design their own tessellation codes based out of Python Turtle (a continued work from yesterday!).  Today, CAMPers’ creativity is highly involved in this self-exploring, 10 minutes project. Anish gives all CAMPers 10 minutes to design a code that forms a tessellation. CAMPers are to create their own project using the knowledge they had before.

In Grace‘s Art Class, CAMPers create their own pull-up net. CAMPers slowly construct the foundation of the net, then forms a foundation of six cube sides. Then, they begin to color each side by drawing tessellations on each cube.

CAMPers create their own tessellation design on the cubes


CAMP Day 5 had been a short yet informative day. CAMPers enjoy their time with their beloved staff. While still having lots of time to use their creativity on every project.

Well done, 2021 CAMPers! Looking forward to meet you all next year!


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CAMP 2021 Day 4 – Tessellations Everywhere!

As usual, welcome to CAMP 2021 Day 4! As we are closing up the week, staffs and CAMPers remain energetic from the early morning. Today, CAMPers work on the in-depth application of tessellation. This includes: complex Voronoi Tessellations creation, constructing tessellations through mathematical understanding, and writing Python Turtle codes.

In Anish‘s Computer Science class, CAMPers learn how to build their own codes on Python Turtle. A Turtle is a pre-installed Python library that allows CAMPers to create pictures and shapes through a virtual background.

Anish’s class begins with a Python Turtle’s introduction.

CAMPers construct their own Turtle codes, take close looks at the Turtle, and write down their guess on what the Turtle will turn out to be.

CAMPers guess what the Turtle codes will end up like.

In addition, CAMPers begin their own journey on Turtle. They write down codes that will lead the Turtle to draw a rectangle in fixed length and width. The turtle runs from one edge to another, CAMPers are to set certain length for it to run.

CAMPers learn how to write a Turtle code to draw rectangles in fixed measurement.
CAMPer’s work on Turtle

In Frances‘s Math Class, CAMPers work on Tessellation Creator, a website that helps CAMPers to build their tessellations online. CAMPers are given information is yesterday’s class about polygons. It is now the time to fit every shapes into one!

CAMPers create Tessellations based on polygons
Student work – create tessellation digitally

In Karen‘s Computer Science Class, CAMPers are introduced to the vertex in programming. They learn how the code endshape” is used to end every shape they create. With this code, many shapes can be created through one canva. Notice how the code “funshape” repeats itself over and over time, the different rotation of the shape itself helps each one fits into one another (just like a puzzle!). 

CAMPers explore the codes and figure out the vertex of each shape

Later on, CAMPers draw shapes and fill out their colors. They create shapes that corresponds with each other – together becomes tessellations

Students can create multiple shapes in the canva

In Grace‘s Art Class,  CAMPers learn about the literal meaning of polygons. They also learn about Voronoi Tessellation – a random sequence of patterns. For instance, city and map views. That said, the World map is also a Voronoi tessellation (see image). 

Definition of polygons!
Our map, if found the right spot, is also a Voronoi Tessellation!
What are some Voronoi Tessellations in real life do you have in mind?
CAMPers working on their Voronoi Tessellations!



Last but not least, we wrap Day 4 with — Among Us! In Ayanna’s Activities, CAMPers enjoy a Mathematics Among Us that is looking for imposters.

As we are getting closer and closer to our last day, CAMPers are more familiar with tessellation and its applications! In the end of the week, we are not ready to say goodbye to CAMP, but what we learn will always carry along with us.


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CAMP 2021 Day 3 – Half Way Through

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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CAMP Day 2 – The Process

It is CAMP Day 2! After having a bright start yesterday, Day 2 begins with CAMPers receiving more knowledge on tessellation.

CAMPers received the CAMP 2021 T-shirt

In Frances‘s Math class, CAMPers created tessellations using a scalene triangle and then examined them to see how they demonstrated that the sum of the angles of a triangle is 180 degrees.  CAMPers then went on to use that information to figure out the sum of angles in any polygon.

Student’s work on tessellation


Student’s work on tessellation based on angles and triangles


CAMPers are asked for what pairs they see on their tessellation works: “Where do the six triangles meet?”

They also label out their works and present them in class. Frances introduces to CAMPers the definition of polygons and different types of shapes (ex. hexagon, octagon, twenty-two gon). 


CS class begins with a review on GeoGebra


In Computer Science class, CS Instructor Karen introduces p5js, a website that allows students to use Javascript to run codes. It allows students to write their own code and run it on the screen


p5js allow CAMPers to run their own codes


CAMPers are introduced to coding languages such as:

function setup ( ){createCanvas(___, ___);}

CAMPers are also introduced and tried out RGB color scheme. RGB stands for red, green, and blue. RGB decides what color it is and gives unique codes to each color. For instance, certain color green will have certain codes. 


RGB color scheme allows different colors to be displayed on the screen


CAMPers also dive into the Pantone website for different color schemes. They later go back to the background color code on p5js.  Background (R, G, B) with RGB set up will give different colors on the screen.

In Shuang‘s Art Class, CAMPers start designing works and prepare for their work presentation. CAMPers create their own collage by ripping paper polygons but not the corner. 


Polygons that will result in different forms, remember not to rip the corner!
CAMPers designing their own collage through the pieces they made before


With the principle, CAMPers can try out different polygons to see what the polygons bring to them. It might bring out different results! A right polygon might bring out a different result with a scalene polygon.

In Grace‘s Art Class, CAMPers talk about how tessellation patterns are used throughout history. CAMPers are introduced to Leo Ming Pei, an artist, and architect who designed the glass pyramid entrance of the Louvre (tessellation!).


Triangles guess game CAMPers enjoy in Grace’s art class


CAMPers browse through images of Mesopotamia, Paris Louvre, Moroccan tiles, and Brazil sidewalks as their art inspirations. In hands-on activities, CAMPers work on their own tiny Louvre tessellation for Zine. The tessellation is built on cubes by use of rotation.

We end Day 2 with many activities that revolve around tessellations, CAMPers are now more familiar with the real-life examples of tessellations!

CAMPer working on an art project


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CAMP 2021 Day 1 – Journey Begins

Today is Day 1 of CAMP! CAMPers join us all around the region this morning. After last year’s virtual CAMP, we decided to host this year’s CAMP online too. Our theme this year is Tessellation.  Tessellation is when a surface is covered by shapes that have no overlaps or gaps.

CAMPers are divided into 6 groups: SIN, SEC, TAN, COS, CSC, and COT, the six functions of angle commonly used in trigonometry. The groups are divided by their grades and the math packets they did during application. The first session (SIN, SEC, TAN) begins from 9:00 am – 1:45 pm, while the second session (COS, CSC, COT) begins from 11:00 am – 3:45 pm. Classes include Computer Science, Math, Art, and Activities.

Beginning from Computer Science Class in the morning, CAMP CS Instructor Karen Blumberg introduces an online tool name GeoGebra. GeoGebra is an interactive geometry, algebra, and statistic application that allows CAMPers to design their own tessellation models.

Karen later introduces the rule that with any segment AB and a randomly located point C, there will always be a connection between segment AB and point C. CAMPers test the proposed rule itself on GeoGebra. 

Segment AB and point C on GeoGebra.

Later on, CAMPers work on forming parallel lines with segment AB that passes through point C on their own screen. The goal for this model is to eventually form a parallelogram. 

CAMPers forming parallel lines with segment AB, connecting point A and point C together to form segment AC.
Final Goal: To create a parallelogram using GeoGebra and the listed rules.

In the afternoon Computer Science Class, CS Instructor Anish Anne leads CAMPers to use GeoGebra to form a tessellation based on parallelograms.

Anish guiding CAMPers to form tessellations


CAMPer’s work in Anish’s class


In Art Class, Art Instructor Shuang Cai introduces how to use origami papers to make an isosceles triangle. CAMPers are given a mission to fold an equilateral triangle using square paper.

Shuang also introduces the final product of CAMP’s Art course – students will create their own Tessellation Zines to share. A zine is a small self-publish work that is full of images or text. In today’s class, CAMPers start making the skeleton of their zine. They learn how to fold an 8-page zine and are shown with an introductory video by Shuang. 

CAMPers learn how to fold their own 8-page zine


Click to watch: Shuang Video

In Math Class, Math Instructor Frances Stern introduces the definition of tessellation to CAMPers. CAMPers are introduced to several examples of tessellation and begin to complete a tessellation of a scalene triangle.

In Activities, HS Volunteer Shoshi Cohen leads a set game with fellow CAMPers. CAMPers are to observe the given patterns and select the three that share similar rules. The rules could be sharing a similar shape or color.

CAMPer enjoying the set game
CAMPers found the sets before through observing the rules


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