Sierpinski Triangle Worksheet

A Sierpinski triangle is an extremely common worksheet that you will find with many different students in any school or college. This worksheet is probably the most commonly used pattern for every class. It also looks very impressive in any style of art and composition. However, it can also be tricky to produce, as it involves counting and directions.

The Sierpinski triangle itself is a series of straight lines drawn within a square, which in turn is divided into four equal rectangles. The first two of these are the left and right sides of the square, while the last is centered in the middle. There are a few different ways to construct a Sierpinski triangle, but the most popular one is by starting at the top and moving clockwise around the outside of the square.

Sierpinski Triangle Worksheet and 24 Best Genius Series Sierpinski Images On Pinterest
Sierpinski Triangle Worksheet and 24 Best Genius Series Sierpinski Images On Pinterest

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Each line you draw on your first turn must be the same length on the second turn, otherwise, you will have an ugly little hole at the bottom of the triangle. Also, as you make your next turn, you should extend one line from the center of the top of the Sierpinski triangle outward so that it passes through the same point that you started the first line at. As you move your pencil around the outside of the triangle, this last line will help you work your way around to the bottom.

To make a Sierpinski triangle from one square, first, you will need to place each square horizontally within the square. Then, fold one of the squares in half from the right. The square you will use as the top portion of the triangle is the one you should place in the middle.

To create a triangle, you will now draw one of the squares from the outside of the square toward the middle. You will repeat this action for the other three squares. Continue with this process until all the squares are in place and they all have three lines running through them.

From each square, you will now trace a line from the bottom of the square to the middle of the square and continue this process around the square until you reach the bottom. At this point, you will have to cross all the lines from the top portion of the triangle to the bottom one.

Sierpinski Triangle Worksheet together with 24 Best Genius Series Sierpinski Images On Pinterest
Sierpinski Triangle Worksheet together with 24 Best Genius Series Sierpinski Images On Pinterest

When you trace your final line to connect the bottom and the middle portion of the square, this will give you a very loose line. You will repeat this process for the other two squares. As you complete each square, you will continue this process until all the squares are completed.

Once you finish the entire Sierpinski triangle, you will need to cross all the lines, pointing from the bottom to the middle. Make sure that you leave one space along the sides of the triangle, but this should not be something that your student is struggling with at the time of the exam. The final step will require your student to read the bottom of the triangle and then recite all of the lines of the triangle at the end of the test.

Sierpinski Triangle Worksheet and Sierpinski Gasket with Control Points Application Center
Sierpinski Triangle Worksheet and Sierpinski Gasket with Control Points Application Center