Convex Hull

Convex Polygon Test

This polygon is convex.

This polygon is not convex.

This is convex lens leadership.

In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.

Check whether this polygon is convex

What does that convex lens do?

So this right over here is what a convex quadrilateral, this is what a convex quadrilateral could look like.

Test whether a given polygon is convex

Construct the convex hull of this polygon

So you have concave, and you have convex.

So one type of convex quadrilateral is a trapezoid.

Now within convex quadrilaterals there are some other interesting categorizations.

A polygon that corresponds to the convex hull of another polygon

So I learned the lesson of convex lens leadership from that.

But river networks look fundamentally different on convex promontories or protrusions.

Convex glass, 10 inches thick, which accounts for the magnifying effect.

Select the polygon of which you want to construct the convex hull...

And the main subdivision of quadrilaterals is between concave and convex quadrilaterals

In Proposition 18 he argues that there are no further convex regular polyhedra.

So this convex quadrilateral would involve that one and that one over there.

Maybe it's made of glass, maybe something else. And I'm going to focus on convex lenses first.

So remember, concave means it opens inward, like a cave. Convex means it kind of opens outward.

If pruney fingers are rain treads, then they should look like the river networks on convex promontories.

So now we're just gonna focus on convex quadrilaterals so that's gonna be all of this space over here.

Since the slope of the convex lens surface increases outwards, separation of the rings gets smaller for the outer rings.

But if all of the interior angles are less than 180 degrees, then you are dealing with a convex quadrilateral.

In the last video, I showed that a bunch of triangles are similar to each other to come up with a relationship between the focal length, the distance of an object from the convex lens, and the distance of the image of an object from that convex lens.

One day he took us out into the sun and tried to show us how to find the focal length of a convex lens.

The Convex Computer series, as well as a number of small scale parallel machines from companies like Pyramid Technology and Alliant Computer Systems were particularly popular.

And in a convex lens, it'll be symmetric. So let me see if I can draw it. One side of the lens will look like that.

In any case, Theaetetus gave a mathematical description of all five and may have been responsible for the first known proof that no other convex regular polyhedra exist.

In mathematics and physics, the Legendre transformation or Legendre transform, named after Adrien Marie Legendre, is an involutive transformation on the real valued convex functions of one real variable.

It is divided in five vertical stripes two white stripes and three black stripes, inside which are the following elements in its upper section, the name of the society superimposed on a white convex section, over golden curvature (gold for honour).

And a trapezoid is a convex quadrilateral and sometimes the definition here is a little bit, different people will use different definitions, so some people will say a trapezoid is a quadrilateral that has exactly two sides that are parallel to each other

These lenses use some form of the cassegrain design which greatly reduces the physical length of the optical assembly, partly by folding the optical path, but mostly through the telephoto effect of the convex secondary mirror which multiplies the focal length many times (up to 4 to 5 times).