Consider a watch face which has identical hands and identical marks
for the hours. It is opposite to a mirror. When is the time as read
direct and in the mirror exactly the same between 6 and 7?
The ten arcs forming the edges of the "holly leaf" are all arcs of
circles of radius 1 cm. Find the length of the perimeter of the
holly leaf and the area of its surface.
An equilateral triangle is sitting on top of a square.
What is the radius of the circle that circumscribes this shape?
In what follows I'm going to call the design above the "unit
shape" and imagine it repeated endlessly along a line - rather like
a stream of paper coming off a roll.
Try to design a new unit shape (probably simpler than mine) to
make a strip which looks the same after a 180 $^\circ$
In other words, make it so that you could not say whether the
torn off strip had or had not been rotated.
First the original strip could have a mirror across it.
This illustration shows the right side as the reflection of the
Can you create a unit shape so that the strip has reflection
symmetry across a vertical mirror line ?
And where would the mirror line need to be to be placed ?