Imagine a circle of rope, which has twelve evenly spaced knots tied in it. Suppose that this rope has been pulled into a taut, triangular shape, with stakes anchoring the rope at knots numbered 1, 4, and 8. Make a conjecture about the type of the triangle.
How do I even draw this? So at first there will be a circle with twelve points on it, but what comes after? Thank you
You could visualize it by looking at the face of a clock and imagining a circle around the face. There would be 12 markings on it (the knots of your string)
the first marking could be 1:00 , the second at 4:00 and the third at 8:00
now count the number of hours between the intervals:
from 1 to 4 ---- 3 hours, so 3 units on your string
from 4 to 8 --- 4 hours, so 4 units on your string
from 8 to 1 ---- 5 hours, so 5 units on your string
Now they form a triangle, obviously scalene
But what else do you notice about the numbers 3, 4, and 5 ?
hint: Think Pythagoras
To draw the given scenario, you can start by sketching a circle. Inside the circle, draw dots to represent the twelve evenly spaced knots. Label the knots from 1 to 12 in a clockwise direction. Then, connect the dots to form a rough triangle shape. Make sure to connect knots 1, 4, and 8 with straight lines to represent the rope anchored by stakes.
Alternatively, you can search for diagrams or images of "12 evenly spaced knots triangle" online to get a visual representation of the triangular shape formed by the rope. This might give you a better understanding of how to draw it.
To draw this configuration, start by drawing a circle to represent the rope. Then, mark twelve evenly spaced points along the circumference of the circle to represent the knots.
Next, draw lines connecting knots numbered 1, 4, and 8. These lines will form a triangular shape, with the rope pulled tightly between the stakes at these knots.
To make the drawing clearer, you can label the knots with their respective numbers (1, 4, 8) and possibly label the sides of the triangle (such as by using lowercase letters like a, b, c) or angles (such as using uppercase letters like A, B, C).
This will help you visualize the triangle and make it easier to make a conjecture about its type.