shouldn't the square's graph lack a point of inflection when y is changing? If the graph is the y coordinate of the shape over a constantly increasing third parameter, I'm pretty sure the square's graph should be straight lines.
What is happening is that the rotation is a set degrees per second so that the three shapes stay in sync. This creates a slight variance in speed along the line of the square making the curve in the graph.
The graph isn't x vs. y. It's distance from center per y. That's why the circle graph isn't constant, and that's also why the square graph is straight at the top and bottom.
If the point going around the perimeter of the square traveled at a constant speed then yes. The slop would be 1 to 1 or 2 to 1 or whatever, but it would graph a straight line. However, here the constant is the angular velocity, and (as previously stated) since the points at the midpoint of the square section are closer than the points at the corners, the speed of the 'point' following the perimeter increases as the distance from the center of the circle increases.
Think of a door on a hinge (as usual). If you are opening a door and you consider a point 1 inch away from the hinge, the angular velocity of that point is considerably smaller than if you consider a point at the end of the door (relative to the hinge), which is about 3 feet away.
Your comment is very close to a perfect explanation, but i think that when you wrote the example of the door, your mind went confused. I think that where you wrote "...,the angular velocity of that point..." you meant the** linear velocity**(or whatever you say in english, i'm spanish), didn't you? That's since you are considering a door opening with constant angular velocity.
Well, if we assume that the line is just spinning around the center of the shape, the dot on the out side of the square fluctuates in speed as the line gets further away from the center and yet has to maintain the constant speed.
Ahh ok. Got it. The third parameter's rate of change isn't constant. The graph is organized so that the angle of the line on the shapes are uniform. Since the square has a larger perimeter, the exterior point has to move faster at certain spots so the angle is the same with the circle so it looks pretty.
A better way would be:
The points on the perimeter of the square are farther away from the center than others, causing a gradual change in speed which makes the diagonal lines on the righthand area squiggly.
In layman's terms if you've passed PreAlgebra:
Treat the line from the center to the outer edge as an angle attached to another line segment that runs from the center to the right in a perpendicular way. The graph to the right is the function value for whatever angle is formed by the rotating line and the fixed one, and creates the waves shown
yes but there's a difference between "basic understanding of algebra/geometry" and writing out a proof for a website that supposed to contain nothing but funny pictures
I took 10 minutes out of my homework filled night to give deeper meaning to a gif than just "oh pretty graph." I'm sorry my nights don't all consist of banging my gf and shallowly drooling over gifs.
sadly enough, my teacher told all of my class to use a little rope to measure the circumference and the diameter of a couple of circles then divide one by the other, before teaching us about pi. I was the only one in the class that didnt get ~3.1415...
lol Everyone was posting science related gifs, so I decided to go with the simpler "shapes" reference. I can imagine this kid thinking, " **** this! I do what I want!"
I'm liking the gifs, but how the hell is this science? that's a very smart bit of engineering, but for some reason people on putting anything that requires the least bit of intelligence or skill under the monnicker "science"
dommazzetti is correct. Corn starch+Water forms a non-Newtonian fluid. Another cool experiment people have done with this mixture is to place it in a long tub, and then "walk on water" by running across the surface before they have a chance to sink.
Any sine graph can be written as a transformation of a cosine graph, but no one calls graphs of these natures "cosine waves" but rather "sine waves" but both of those terms really imply the same thing.