| A simple way to show that the inside angles of a triangle are equal to half a circle is to imagine walking round it. |
| When you have walked right round anti-clockwise you have turned 3 corners to the left and you are facing the way you started so those 3 corners must add up to a full circle. If you had turned right back on yourself to the right at the corner that would have been a half circle. So, of the 3 circles drawn at the three corners there are three half circles outside of the triangle and another three angles which add up to a full circle making a total of two and a half circles outside leaving exactly half a circle for the inside angles. Back to the pentagon and the golden mean |
