stiffness

Stiffness

Stiffness variance

That's the secant

Just a little stiffness. That's all.

Got even smaller, the secant

So the slope of the secant

So the slope of my secant

So that is the slope of this secant

That's not guessing. The child has a fever, headache, stiffness.

And we got the slope of the secant line.

So let's figure out the slope of this secant

So my slope of my tangent of my secant

So this is the slope of the secant line.

The slope of the secant, let me write that properly.

So the limit as h approaches 0 of my secant slope.

But if delta x got a little bit smaller, then the secant

So what is the slope going to be of the secant line?

line FG. And the line that intersects at two points we call this a secant of circle A. It is a secant line to this circle right here.

So the limit as delta x approaches 0 of our slope of the secant

So maybe a good start is to just say, hey, what is the slope of this secant line?

And if I were to actually draw it out, it would actually be a secant line between, to the curve.

If I took h to be even a little bit smaller, I'd be finding the slope of that secant line.

like Richard, or a cockroach, or a crab, or a kangaroo, the relative leg stiffness of that spring is the same for everything we've seen so far.

Obviously, if h is a large number, my secant line is going to be way off from the slope at exactly that point right there.

So, you know, first, maybe h is this fairly large number over here, and then if I take h a little bit smaller, then I'd be finding the slope of this secant line.

It's an observation with obvious medical applications in humans as well, but it's also relevant in a broad sense, I think, to the design of prosthetics, soft robots, basically anything where changes of shape and stiffness are important.

The slope of the secant line is equal to the value of the function at this point, f of x naught plus h, minus the value of the function here, mine f of x naught.

So if you're ever thinking about the issue of compliance, when we're talking about stiffness, think about these curves and the fact that where the slope is tells you how compliant something is, and that arteries are going to be more compliant than a stiff pipe, certainly, but less compliant than the veins.

This painting is often compared to an early renaissance painting by Raphael's teacher Perugino The Giving of the Keys to Saint Peter and you can begin to see here in this early work by Raphael indications of what we understand now as the high renaissance style as opposed to the kind of stiffness of the 15th century of the early renaissance.