The circle is made from two connected 1-d waves, each moving the horizontal and vertical direction.īut remember, circles aren't the origin of sines any more than squares are the origin of lines. ( Source: Wikipedia, try not to get hypnotized.)Ĭircles and squares are a combination of basic components (sines and lines). We often graph sine over time (so we don't write over ourselves) and sometimes the "thing" doing sine is also moving, but this is optional! A spring in one dimension is a perfectly happy sine wave. Quick Q & AĪ few insights I missed when first learning sine: Most textbooks draw the circle and try to extract the sine, but I prefer to build up: start with pure horizontal or vertical motion and add in the other. we have a circle!Ī horizontal and vertical "spring" combine to give circular motion. Time for both sine waves: put vertical as "sine" and horizontal as "sine*". Sine that "starts at the max" is called cosine, and it's just a version of sine (like a horizontal line is a version of a vertical line). 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.
#WAVES X NOISE CREACKED SIMULATOR#
Let's observe sine in a simulator (Email readers, you may need to open the article directly): 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.
![waves x noise creacked waves x noise creacked](https://whylogicprorules.com/wp-content/uploads/2020/04/Screenshot-2020-04-07-14.00.21.png)
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".
![waves x noise creacked waves x noise creacked](https://dt7v1i9vyp3mf.cloudfront.net/styles/news_large/s3/imagelibrary/R/RestorationShootout_05-o0wDhGIT49rcx4Pk245uU7N8nfABZYrC.jpg)
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.
![waves x noise creacked waves x noise creacked](https://lh6.ggpht.com/-eU25bnK_xMY/UIFV4gSKD_I/AAAAAAAACwI/wbW3qPxd87E/Xnoise%2520Linux_thumb%255B2%255D.png)
![waves x noise creacked waves x noise creacked](https://www.aps.anl.gov/sites/www.aps.anl.gov/files/APS-Uploads/APS-Highlights/sound.jpg)
Yes, I can mumble "SOH CAH TOA" and draw lines within triangles.