Any one of them could have been visible to all the stations at once. So geometrically , they could all be the culprit. But that's where the trail started to go cold.
And so it's possible to do that. And geometrically what's going on is that there's always sort of light rays. So like if this wave represents light, for example, you can imagine this wave as the superposition of photons all traveling at the speed of light.
And it sounds pretty easy. It's actually a little bit tricky geometrically . And that just shows as your sandwich-- I mean, triangular sandwich, hexagonal sandwich, et cetera, and sort of the asymptotic behavior of your eating.
and then rotate it through an angle theta, that rotated point is the same as multiplying by e to the i theta. So e to the I theta geometrically corresponds to a rotation by an angle theta in the complex plane. So that means we can interpret this geometrically as a rotation by one turn as 1.
So e to the I theta geometrically corresponds to a rotation by an angle theta in the complex plane. So that means we can interpret this geometrically as a rotation by one turn as 1. So in other words, if you rotate by a full turn, you just get back to where you started.
So this is a concept that sometimes gets referred to as the horizon, we refer to as the interval. some indefinite future that is geometrically discounted.
So this is a concept that sometimes gets referred to as the horizon, we refer to as the interval. One is that we don't always geometrically discount our payoffs.
So you can see when we're pushing sort of on the pixel, you can push and hold, and you can measure sort of the lightest finger taps all the way to very, very So we try to accommodate that geometrically by building highly serpentine traces where we can accommodate sort of longitudinally or torsionally
So an eclipse works. Here's what's happening. During an eclipse, geometrically , the moon gets in front of the sun. And therefore, the shadow of the moon makes a dark spot on the Earth.
I'm actually going to give you a little bit more of an assignment. Not only do that algebraically, but you should also do that geometrically . What's on the left hand side is a square.
And in his physics, he did that by doing the mathematics a little differently than other people. You can do-- a lot of physics has either had to be done algebraically, or with functions, or geometrically sort of with pictures. And it's kind of like the difference in high school between algebra and geometry.
triangle or the six pointed starfish. So, it enabled him to abstract the idea of symmetry underlying something and this is perfect now when we go to the Alhambra. Because if we look at the tiles on the walls in the Alhambra, how can we say when two of those walls have the same underlying symmetry? Now, they might look geometrically very different but Galois's language enables to say actually the symmetries of these two walls are the same symmetries, although they look very different. So, we've got this beautiful walls with these little
and ended up in satellites in orbit now right now. So our fingerprints, if they didn't clean them up very well, they're in orbit right now -- similar kind of shape, about the size of toilet paper tube, and geometrically -designed to collapse a certain way. Hand-folded, sent off for gold coating.