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Posts tagged math

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As long as they know the basic idea - that, in the given example, there is fifteen 23’s or twenty-three fifteens - why not? Some students will take to this method, some will prefer the other ways (abacus, Singapore math, etc). They should be exposed to all of them :-)


hacking-curriculum:

diverse perspectives inform how we might teach basic skills

(Source: theinturnetexplorer)

92815 notes #math #teaching

Mar13

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 keep using the angle from the x-axis 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. In other words, the speed of the dot around the polygon is not constant anymore. 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 keep using the angle from the x-axis 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. In other words, the speed of the dot around the polygon is not constant anymore.

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

153121 notes #math #art

Feb7

jtotheizzoe:

Sphereflakes

I’m pretty comfortable guessing that you haven’t considered the 3D symmetry present in snowflakes before, because who has? We consider them two-dimensional objects, but when you start to imagine a world with exotic planes of snowy symmetry … it gets pretty mind-blowing.

You’ve done it again, Vi Hart.

Previously: Here’s Vi’s original paper snowflake video, which takes them to another level. I even made some!

188 notes #science #math #art #projects

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