A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).
The three corners of a triangle are sitting on a circle. The angles
are called Angle A, Angle B and Angle C. The dot in the middle of
the circle shows the centre. The counter is measuring the size of
Angle A in degrees. What is the smallest Angle A can be? What is
the largest Angle A can be? What else do you notice about Angle A
as you move the corners of the triangle around the circle?
This solution is from David Jeffreys
I think I have worked out the answer to getting an angle.
What you do is fold the paper in half (lengthways). Next you
fold another so the crease touches a top corner (If you hold it as
a landscape) and the corner below it touches the first crease.
The second layer at the bottom corner is 60 degrees. If you want
to make it into an equilateral triangle you fold the over side so
the fold has the other fold tucked right in and align it up with
the other edge.
David supplied some diagrams like the one below.
The angles are 30 o and 60 o can be seen
if you consider an equilateral triangle of side 2a: