Draws ellipses and circles

These ellipses only came about because

Anyway that's a little bit on ellipses.

Their projected surface brightness profiles look pretty close to ellipses.

It's pretty clear that circles and ellipses are somehow related.

And I even know a little bit about ellipses and hyperbolas.

I'll leave you there, I'll continue this in the next video where I'll talk a little bit about ellipses.

And again, error ellipses overlap and all zoom in onto the region where vacuum energy density is about 73 .

line of the ellipses like these, but you certainly cannot fit a more complex data set like that shown here.

But note that these error ellipses are pretty large and they do not really nail down the exact cosmological model.

Such an educational system is against evolution, it makes the human species go forward... not in a straight line, but in ellipses.

And you can obviously see that elliptical galaxies really do look like ellipses, although, ellipticity may be changing as a function of radius.

So that the minimum, so the bottom of the bow is this point right there, right? This middle, the middle of these concentric ellipses.

In the next couple of videos I'll do a bunch of problems where we draw a bunch of hyperbolas, ellipses, and circles with actual numbers.

So, this is very, very tall and skinny ellipses, or these very tall skinny ovals, can form the contours of the cause function J of theta.

And by doing it at that angle, if you've got that misconception in your head, then that two dimensional representation of a three dimensional thing will be ellipses.

And imagine a bow shape that sort of grows out of my screen like this, so that each of these ellipses, you know, has the same height above my screen.

Essentially, what that means is the error ellipses now rotate, and from multiple measurements, you can deduce A lot about, geometry, even without re, resorts, to the other measurements like supernovae.

And what Bayes' rule says is that I should multiply the numbers on the red by the numbers on the green to get the numbers of the yellow, which have the ellipses, and that's my belief.

And this is where it's useful to find a point where you can kind of get the intuition, and we did it with the ellipses, where we said if we take these points, we used logic in the

There's some degeneracy which means essentially that lot of them will be coupled together and in this particular case error ellipses are highly elongated along the line that's almost parallel to the flat universe line in the old diagram of omega matter versus omega vacuum.

Which is why we think the universe is very close to flat so that degeneracy can be broken by a different measurement which would have error ellipses that are not oriented in the same way and you may recall that those from supernova measurements looked pretty much orthogonal through this.

Where this distance and notice the similarity here with the ellipse this distance right here let me do it in a more vibrant color this distance right here, between these two I guess you could call them the elbows of the two ellipses that distance right there, that is a, and this is also a.