Inside a regular pentagon , construct 5 more regular pentagons of side length . The part of the overlapping of these pentagons yields another regular pentagon of side length .
Let . Find .
Above shows a 18-sided regular polygon. How many obtuse triangles are there formed by 3 vertices?
The figure in the above sequence is constructed by the following procedure:
Let be the total blue area of the figure in the sequence.
Compute .
It is not easy to draw a regular decagon without tools.
On a piece of writing paper (with equally spaced lines), I am trying to draw a regular decagon, as shown above. I started by drawing two sides so that their vertical extent is precisely 1 unit of the paper (black lines).
Now I want to draw the next side (red line), and I wonder how far it will extend vertically. To 3 decimal places, what is the distance marked with a question mark?
A regular octagon has squares and inscribed in it. These squares form a smaller octagon as shown.
Let the the area of octagon be and the area of the smaller octagon be . Then for some integers and , where is square-free, Find .