![]() ![]() This time, we start at the max and fall towards the midpoint. There's a small tweak: normally sine starts the cycle at the neutral midpoint and races to the max. See him wiggle sideways? That's the motion of sine. In the simulation, set Hubert to vertical:none and horizontal: sine*. But seeing the sine inside a circle is like getting the eggs back out of the omelette. Let's watch sine move and then chart its course. Does it give you the feeling of sine? Not any more than a skeleton portrays the agility of a cat. This is the schematic diagram we've always been shown. No, they prefer to introduce sine with a timeline (try setting "horizontal" to "timeline"):Įgads. Unfortunately, textbooks don't show sine with animations or dancing. It's the enchanting smoothness in liquid dancing (human sine wave and natural bounce). Sine changes its speed: it starts fast, slows down, stops, and speeds up again. It's the unnatural motion in the robot dance (notice the linear bounce with no slowdown vs. Linear motion is constant: we go a set speed and turn around instantly. Let's explore the differences with video: Big difference - see how the motion gets constant and robotic, like a game of pong? Go, Hubert go! Notice that smooth back and forth motion? That's Hubert, but more importantly (sorry Hubert), that's sine! It's natural, the way springs bounce, pendulums swing, strings vibrate. Sine clicked when it became its own idea, not "part of a circle." ![]() Remember to separate an idea from an example: squares are examples of lines. Let's build our intuition by seeing sine as its own shape, and then understand how it fits into circles and the like. In a sentence: Sine is a natural sway, the epitome of smoothness: it makes circles "circular" in the same way lines make squares "square". Circles circles circles."Īrgh! No - circles are one example of sine. But a line is a basic concept on its own: a beam of light, a route on a map, or even-Īlien: Bricks have lines. see that brick, there? A line is one edge of that brick. You: Geometry is about shapes, lines, and so on. I was stuck thinking sine had to be extracted from other shapes. ![]() Yes, I can mumble "SOH CAH TOA" and draw lines within triangles. ![]()
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