This artifact is known as a right triangle, or R.A.T (Right Angle Triangle). Do you see that little square in the corner? That's a 90° angle. This angle is made up of things called legs. At the other two corners of the triangle are two other angles, theta and beta. These two angles together make another 90°, therefore they are called complimentary angles. The longest side of the triangle is known as the hypotenuse.
This next artifact, as you can plainly see, is a square. The lines on each of the 4 sides show that each of those sides are equal to the others. This square has 4 90° angles, so the total of all the angles is 360° (90° x 4 = 360°). If you cut this square in half diagonally, we get two right triangles, the same as the first artifact.
This is a sculpture of Pythagoras, a man who was born in Greece. He was considered the father of Math, Geometry, and Philosophy. Something he was very interested in was harmonics, and he associated this with a lot of the work he did. His work includes inventing the Pythagorean Theorem, giving proof that the changes from Day to Night are caused by the Revolution of the Sun, and figuring out the circumference of the Earth. He was fluent in Egyptian, trained in the finest academies in Persia, as well as a Vegan (someone who doesn't eat anything living). His death occured around age 90 of unknown causes.
The last picture here is of the Pythegorean Theorem. This theorem stated that if you added a square on both legs of a triangle and the hypotemuse, the area of both the squares would equal the area of the square on the hypotemuse.
Truthfully, I'm not 100% sure why Harbeck cares about this in Grade 8 Math. I doubt I'm going to be using it in say, 10 years, but you never know. Everything is taught for a reason, might as well make the most of it.
To add on to what I've said above, here are two videos that Jessica and I created to show the Pythagorean Theorem. Enjoy!