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trigonometry

Conic Sections (Desmos)

EDITED:  Thanks to the wonderful folk at Desmos, who helped me solve my problem within minutes of tweeting it, I now have fully functional models.  The problem was making the black dotted distance lines only point to the relevant focus/directrix and not both.  Writing lines parametrically – that’s how to impose conditions on when they appear.

I’ve been trying to make some models to show the relationship between the curve, focus and directrix on conic sections, Continue reading “Conic Sections (Desmos)”

Projectile Motion (Desmos)

You can do a simple model of projectile motion in Desmos and create sliders to alter the angle and speed of projection in order to see how these affect the motion.  Make sure you have angles set to measure in degrees (settings, above zoom, right-hand side).

Flight and Fight

Back in 2010 I, and 12 million other people, became slightly addicted to a little game called Angry Birds.  I stopped playing after a couple of months, like I always do with these things, not sure what happened to it then, probably petered out like so many other overnight success stories.

The premise of the game was to get your little birds to destroy some nasty green piggies who were stealing your eggs by launching them from a slingshot at the pigs’ defences.  I can see why those birds were angry, I would be if I were repeatedly being launched, projectile-style, at towers of wood and ice and stone.  That’s gotta hurt.

The programmers use some fairly simple mathematics to get those birds to move in a realistic way.  You intuitively expect the birds to move through the air in the way they do because all objects move like that, unless some force causes them to change their path.  Picture it now – imagine throwing a tennis ball, what shape does the path of the ball take? What about a diver jumping off a diving board, or a bullet flying through the air, or water spouts from a fountain? Continue reading “Flight and Fight”

Good Vibrations

It was King Solomon who lamented that “there is nothing new under the sun”.  This is borne out again and again: story plots, terrorism, facial hair, blog posts, popular music.  Let me demonstrate the latter to you, or rather, let Axis of Awesome demonstrate it:

Next time you listen to the radio, you’ll hear those chords.  In fact, you’ll notice it a lot now you’re aware of it.  This is called the Baader-Meinhof phenomenon, like when you settle on which new car to buy, and suddenly it’s everywhere. Continue reading “Good Vibrations”

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