Please help me. I have cut up the paper and followed the directions, I do not know what mathematical truth this is. help help help. I don't understand this. the problem is below:
Cut a piece of paper to form a triangle shape. Tear off the three corners of the triangle. Then put the three corners together. Describe what you see. What mathematical truth does this activity illustrate?
Hi, Lucy, this is Matthew's mom, if you put the three corners together you would get 1/2 a circle or circumference. I hope this helps you.
To understand the mathematical truth behind this activity, let's break it down step by step.
Step 1: Cut a piece of paper to form a triangle shape.
To cut a piece of paper into a triangle shape, you can start by selecting a rectangular piece of paper. Then, fold it diagonally from one corner to another, creating a right-angled triangle. Finally, cut along the folded line to separate the triangle from the rest of the paper.
Step 2: Tear off the three corners of the triangle.
The next step is to tear off the three corners of the triangle. You can tear off each corner by folding the triangle in half and ripping it along the crease, which should create three smaller triangular pieces.
Step 3: Put the three corners together.
Now, take the three torn corners and align their edges to form a new shape. Try different arrangements, such as placing them side by side or lining them up at different angles.
By going through these steps, what you should observe is the formation of a quadrilateral (a polygon with four sides). This quadrilateral is called a "reuleaux triangle" or a "curvilinear triangle."
The mathematical truth illustrated by this activity is that it is possible to create a shape with constant width, even though it is not a circle. The reuleaux triangle has the special property that its width remains constant, meaning that no matter how the shape is oriented, a straight line can pass through the shape touching all three corners at some point.
This property of constant width is not only intriguing but also has practical applications. For example, it is used in engineering to design objects like camshafts, drill bits, and wrenches that can fit into circular openings while still having a larger range of motion.
So, in summary, by cutting a triangle shape and rearranging its corners, you create a reuleaux triangle, which demonstrates the mathematical truth of a shape with constant width.