When is the ppc curve convex

Convex square - a simple explanation and examples

You should draw or edit a convex square. Even if it looks like math jungle again, the task is actually quite simple.

What you need:

  • actually just a little time

The term "convex" in geometry - an explanation

Your task probably fails because you do not know what the term "convex", which comes from mathematics, means.

  • Perhaps you already know the term from optics, because it deals with convex lenses. These are outwardly curved lenses, i.e. typical converging lenses.
  • The term has a similar meaning in mathematics. Functions and geometric figures can also be convex, i.e. curved outwards.
  • Incidentally, it is very easy to examine whether this applies to a figure with straight or curved boundaries: the figure is convex if you can connect every point on the boundary line with every other point with a straight line in such a way that this route goes completely through Figure goes.
  • For example, every triangle with straight edges is convex, because such connecting lines will always lie within the triangle, regardless of which two points on the edge of the triangle you connect. And of course every circle is also convex, since it only has a boundary that is always curved outwards.

A convex square - examples and counterexamples

  • With a square the situation is more complicated. The common squares and rectangles (with straight edges!) Are undoubtedly a convex rectangle, because all points can be connected to all points in such a way that the line lies within. So if you are to draw a convex rectangle, a simple square already fulfills this task.
  • The usual parallelograms, trapezoids and dragon squares are also convex squares, as you can easily check for yourself.
  • But what about a general figure with four corners? In principle, these are created by expanding any triangle by a fourth corner and thus forming the edges of the square.
  • However, if this fourth point lies within (!) The triangle, an indentation is created in the square at this point. Such quadrilaterals are of course not convex, for example you cannot connect the two (then) outer corner points with a line that lies completely within the indented quadrilateral.
  • Do you want the square to have curved edges? No problem either - with a normal straight-edged square you only have to "bend" these edges outwards, ie create a convex edge (see above).

By the way: the star pentagon is the best known non-convex figure.

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