Postman

Putting my own personal stamp on the world

40 notes

bumplerton:

So I was at this music store and I found this unofficial tool album with a close up of Maynard’s face. I took one look at the title of the cd and started laughing hysterically

OPIATE!! ohmygoshohmygoshmohymsgosh

bumplerton:

So I was at this music store and I found this unofficial tool album with a close up of Maynard’s face. I took one look at the title of the cd and started laughing hysterically

OPIATE!! ohmygoshohmygoshmohymsgosh

396,008 notes

1ucasvb:

The familiar trigonometric functions can be geometrically derived from a circle.
But what if, instead of the circle, we used a regular polygon?
In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1.
We still want to stick to using the angle from the horizontal as the function’s input, instead of the distance along the polygon’s boundary. (These are only the same value for the circle!) This is why the square does not trace a straight diagonal line, as you may expect, but a segment of the tangent function.
Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon.
More on this subject and derivations of the functions can be found in this other post
Now you can also listen to what these waves sound like
This technique is general for any polar curve. Here’s a heart’s sine function, for instance

1ucasvb:

The familiar trigonometric functions can be geometrically derived from a circle.

But what if, instead of the circle, we used a regular polygon?

In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1.

We still want to stick to using the angle from the horizontal as the function’s input, instead of the distance along the polygon’s boundary. (These are only the same value for the circle!) This is why the square does not trace a straight diagonal line, as you may expect, but a segment of the tangent function.

Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon.

More on this subject and derivations of the functions can be found in this other post

Now you can also listen to what these waves sound like

This technique is general for any polar curve. Here’s a heart’s sine function, for instance