A shape is convex if a line segment that is drawn between any two points in the shape is completely contained within the shape.^{[1]}

Figure 1 is an example of a convex shape, in this case a disc. Since it is not possible to pick two points within the shape and draw a line between them that leaves the shape, the shape is convex.  

Figure 2 is an example of a concave shape. Note that the entire line is not contained within the disc.  
Discovery  Is a spherical solid convex or concave?A spherical solid is a three dimensional shape with a sphere as the outer edge. Is a spherical solid concave or convex? Imagine a sphere. Can you imagine a straight line between any two points in the spherical solid that is partly outside the solid? Click here to see the answer. A sphere is convex. Mnemonic What is a mnemonic?StoryA bear wanted a nice cozy cave in which to spend the winter. She found a rock sticking out of the ground, but it vexed her that the rock was convex. She continued to look. Then she found a cave. It was concave, so she crawled in and went to sleep for the winter. 
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