Often curves in two dimensional (plane curves) or three dimensional (space curves) Euclidean space are of interest.

AAVSO Light Curves...

These two curves are averages

AAVSO Light Curve Generator

Well we already know that definite integrals can help us figure out areas underneath curves or between curves.

A straightedge is to draw these lines. A compass is to draw these curves.

It's something that is totally out of the bell curve.

So we have these two curves.

They didn't say, Our style is curves. Let's make the house curvy.

Calculus is also a mathematics of curves.

But squarecut or pearshaped These rocks don't lose their shape

Squarecut or pearshaped These rocks don't lose their shape

I'm now going to use definite integrals to figure out the areas under a bunch of curves and, if we have time, maybe even between some curves.

It turns out one of the interesting curves for startup companies is a technology

You can take all kinds of curves, and they're all pointing up.

And I think that that's what we're seeing here in this explosion of curve.

So we want to figure out the area between these 2 curves.

This is a little thing that I made because I really like the idea of curves and balls together.

I have some curve C that looks something like this.

Curves and bam, hits the other 0, hits the y intercept, and then goes back up like that.

And Demps, all 5,000 of them are strung out from here to Texas.

This made no sense at all, so they consigned these curves to the back of the math books.

They said these are pathological curves, and we don't have to discuss them.

A man named Peano did define such curves, and it became an object of extraordinary interest.

And what it is, is working with both positive and negative space but also with these curves.

lots of other curves that we've seen, goes along a depletion curve.

Then after we harvest a coral, we measure this ratio, and now you can see, those curves match perfectly.

But there's kind of 3 types of interesting points on most of the curves we'll talk about.

Their popularity rose in the United Kingdom with the release of their second album, The Bends (1995).

This was the earliest book in which these curves are considered and defined as curves of the second degree.

Two lines, I mean that can happen with curves, but that's not going to happen with lines.

Because it's also useful in studying curves, pi helps us understand periodic or oscillating systems

Now the question that I'd like to ask is, if you look at these exponential curves, they don't go on forever.

It almost looks like two parabolas, but not quite, because the curves look a little less U ish and a little more open.

So the price of oil, much like lots of other curves that we've seen, goes along a depletion curve.

It shows two black holes in orbit around each other, again, with these helpfully painted curves.

If we were to focus on reconstructing these curvy lines on the map, infrastructure, that cross the straight lines, the borders,

But anyway, my question to you, or my question to myself, really, is what is the area between the curves where they intersect?

He was a prodigy at the age of twelve he wrote a memoir on four geometrical curves and under his father's tutelage he made such rapid progress in the subject that in his thirteenth year he read before the Académie française an account of the properties of four curves which he had discovered.

These two curves are averages Standard Poor, the blue one and the red one is Standard Poor's from which the five biggest discontinuities are taken out.

Now, as if this was not enough to just bend the curves and understanding the accelerated pressure on the planet we also have to recognize the fact that systems do have multiple stable states, separated by thresholds illustrated here by this ball and cup diagram, where the depth of the cup is the resilience of the system.

This is really interesting, because you might have heard about startups about something called the hockey stick, and the hockey stick is actually this kind of curve.

These curves for global temperature, atmospheric CO2 and sea level were derived from ocean cores and Antarctic ice cores, from ocean sediments and snowflakes that piled up year after year over 800,000 years forming a two mile thick ice sheet.

No, I'm not showing you any images, because black holes don't leave behind helpful trails of ink, and space is not painted, showing you the curves.

Honored in obituaries in newspapers around the world as the man who revolutionized modern architecture by adding curves and levity to buildings and constructions in hundreds of architectural projects in Brazil and abroad.