The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
A circular plate rolls in contact with the sides of a rectangular
tray. How much of its circumference comes into contact with the
sides of the tray when it rolls around one circuit?
Four jewellers possessing respectively eight rubies, ten saphires,
a hundred pearls and five diamonds, presented, each from his own
stock, one apiece to the rest in token of regard; and they thus
became owners of stock of precisely equal value. Tell me the prices
of their gems and the values of their stocks. (Editors note: In
this problem you are only given enough information to find the
values of rubies, saphires and diamonds relative to the price of a
The areas of three of the triangles are shown.
What is the area of the quadrilateral $APOQ$?