## Introduction: String Art Cardioid Using Two Times Table

After having a look at the wonderful entries in the made with math contest i was awe struck by the creativity and uniqueness of projects but unfortunately all of the projects were compatible with person having age of 13 or plus since the use of higher level mathematics or other tools which a student of smaller age can't use. I wanted to build something that will be enjoyed by any age group (minimum age 8+ with a little supervision of adults).

In this instructables we are going to make a string art by using 2 times table. This instructables might help students memorize times tables in a amazing practical way.

So lets get started.

## Step 1: Supplies

- Woolen thread
- Nails/paper pin
- Hammer
- Plywood(300mm*300mm*4mm)
- Glue
- A3 paper sheet
- Pencil
- Eraser
- Ruler
- Compass
- Protractor
- Scissors

## Step 2: What Is Cardioid ?

cardioid is a mathematical shape resembling a heart. A cardioid shape can be created by following the path of a point on a circle as the circle rolls around another fixed circle, with both of the circles having the same radius.The name was coined by de Castillon in 1741.It is shaped more like the outline of the cross section of a round apple without the stalk. Cardioid can also be seen in a cup as shown in the picture.

source:(https://en.wikipedia.org/wiki/Cardioid)

## Step 3: Base Circle

Let's start with drawing our base circle on A3 sheet.Find the approximate center of the sheet by folding horizontally and the vertically as shown in the pictures. Mark the center with pencil make sure the pencil is sharp throughout the instructable. The pencil mark should be as light as possible but should be visible. Use compass and determine the diameter of circle to be drawn.

Here i am drawing the circle of diameter 280 mm.

We know diameter is 2 times radius.

Therefore r=d/2

r=280/2=140 mm

Use a ruler and point one end of the compass at zero and other at 140 on the ruler as shown in the picture. Draw the circle by setting the center point of the circle as the center of the A3 sheet.

## Step 4: Points for Nails

In this step we will divide the circumference of the circle into equal parts, this totally depends on you. Here i am dividing the circle into 60 equal parts.

A circle has 360 degrees.

We want to divide the circle into 60 equal parts having equal degrees spacing.

So the math work's out as,

(360/x)=degrees in one part

Where x is no of parts in the circle

(360/60)=6 degrees in one part

Now place the center of protractor coincidentally on the center of the circle while aligning the zero line of the protractor on the start line of the circle. Mark points after every 6 degrees starting from 0 degrees. You can use the protractor with whole 360 degrees or the standard one with 180. When using the 180 degrees standard protractor mark the end point ending at 180 degree. So the total points marked will be 30.

Now we will be extending the point on the circumference of the circle. Place the ruler such that center of the circle and the marked point are linear while keeping in mind that ruler is intersecting on both side of the circle's circumference. In this way we will get 2 points on the circumference of the circle with one marking point.

After dividing the circumference into equal 60 parts start numbering it from 0 to 59. Mark the number 60 above the number 0 and once again start marking numbers form 60 to 119. Mark point 120 above point 60. Make sure the numbering are lightly marked we will be erasing it afterwards.

## Step 5: Base for Nails

Apply glue on the plywood and stick the base circle pattern on the plywood. Let the paper dry.

If the plywood is not of the desired dimension use a adult persons help to cut the plywood just bigger then the base circle with numberings. It doesn't matter if the plywood is not good looking as in my case since the paper is going to camouflage the wood.

## Step 6: Nailing It!

This step requires adults help if you are below the age of 10 years.

Start hammering nails on marked sections on the circumference of the circle.Make sure the nails are straight and perpendicular to the surface and are not going through the plywood.

## Step 7: The Art With Math

In this step we are going to start the process of string art.

As the title suggests,the art is going to be made with the help of 2 times table.

The starting number of the base circle is 0 so 2 times 0 is equal to 0.

2*0=0

Tie the loose end of the woolen string to the nail corresponding to the number 0. Now move towards the next number that is 1 and make a loop of the string on the nail corresponding to number 1.

Now as we are on number 1 multiply it by 2,so 2 times 1 is equal to 2.

2*1=2

As the answer is 2 make a loop of string on the nail corresponding to number 2.

Now as we are on number 2 multiply it by 2,so 2 times 2 is equal to 4.

2*2=4

As the answer is 4 make a loop around the nail corresponding to number 4. Note here we are jumping the number 3 as the starting point is 2 and end point is 4. After making loop on nail 4 move back to the preceding starting point i.e 2 and tie a loop. After making loop on point 2 move to the next point 3 and make loop.

Now as we are on number 3 multiply it by 2,so 2 times 3 is equal to 6.

2*3=6

As the answer is 6 make a loop around the nail corresponding to number 6. Note here we are jumping the number 5 as the starting point is 3 and end point is 6. After making loop on nail 6 move back to the preceding starting point i.e 3 and tie a loop. After making loop on point 3 move to the next point 4 and make loop.

Now as we are on number 4 multiply it by 2,so 2 times 4 is equal to 8.

2*4=8

As the answer is 8 make a loop around the nail corresponding to number 8. Note here we are jumping the number 7 as the starting point is 4 and end point is 8. After making loop on nail 8 move back to the preceding starting point i.e 4 and tie a loop. After making loop on point 4 move to the next point 5 and make loop.

Continue the steps till you arrive at the last number 60 and tie a knot to the nail.

2*60=120

Make sure the string are in tension or else the aesthetics of the art will be ruined,however don't pull the strings too much which may lead to plucking of the nails.

Cut the string using a scissor.If you fear the knot will untie put a drop of super glue on the knot which will securely hold the knot on the nail.

## Step 8: Start and End Points

2*X=Y

where X is start point and Y is end point

start-- end

2*1= 2

2*2= 4

2*3= 6

2*4= 8

2*5= 10

2*6= 12

2*7= 14

2*8= 16

2*9= 18

2*10= 20

2*11= 22

2*12= 24

2*13= 26

2*14= 28

2*15= 30

2*16= 32

2*17= 34

2*18= 36

2*19= 38

2*20= 40

2*21= 42

2*22= 44

2*23= 46

2*24= 48

2*25= 50

2*26= 52

2*27= 54

2*28= 56

2*29= 58

2*30= 60

2*31= 62

2*32= 64

2*33= 66

2*34= 68

2*35= 70

2*36= 72

2*37= 74

2*38= 76

2*39= 78

2*40= 80

2*41= 82

2*42= 84

2*43= 86

2*44= 88

2*45= 90

2*46= 92

2*47= 94

2*48= 96

2*49= 98

2*50= 100

2*51= 102

2*52= 104

2*53= 106

2*54= 108

2*55= 110

2*56= 112

2*57= 114

2*58= 116

2*59= 118

2*60= 120

## Step 9: Final Thoughts

This art requires practice and patience,a single mistake will ruin the whole art so i would recommend first to practice on a blank sheet by drawing lines by pencil where the strings would come and then proceed to making the actual art design.

Now you might be wondering what do we get when we use times table other than 2.

I am linking the video from where i was inspired to make this art,do check out this video which shows different shapes we obtain when we use different times tables it also explains cardioid further in detail.

Times Tables, Mandelbrot and the Heart of Mathematics

After making this art gift it to your mathematics teacher or your loved ones who loves math.

If you are going to make it tell me in the comment section

I am uploading a stop motion video of my build if you want you can download the file and watch it.

Runner Up in the

Made with Math Contest