Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.
The Earth is further from the Sun than Venus, but how much
further? Twice as far? Ten times?
When we measure something we use a scale : we consider the size
of one thing in terms of another.
Make a fist with your hand (it's about the size of a large
orange isn't it?), and then locate a point about 10m away from
If your fist was the Sun, the Earth would be more than 10 metres
away and less than 1 mm in diameter (the tip of a ball-point
Venus orbits the Sun three times in roughly two Earth years. On
rare occasions Venus can be seen (from Earth) passing across the
face of the Sun, this is called the Transit of Venus.
Usually Venus appears to pass either above or below the Sun
because the plane of Venus' orbit is slightly tilted to the Earth's
own orbit around the Sun. The Transit of Venus has only been
observed and recorded six times since telescopes became available
early in the 17th century.
Perhaps you remember The Transit of Venus happening in 2004, it
will happen again in 2012.
The Transit of Venus was a valuable observation because it
provided the data with which the Earth to Sun distance could be
calculated. This distance is called the Astronomical Unit and is
used like a scale for the Solar System.
But even without a Transit of Venus to provide data astronomers
could know the ratio between the Venus to Sun distance and the
Earth to Sun distance. What could they observe and what calculation
would they need to do?
Google will give you all sorts of interesting things connected
with the Astronomical Unit and the Transit of Venus, you may also
enjoy looking at this link to the Motivate
Project , but before you do that imagine you are living in the
17th century and don't have the internet, how might this Venus to
Sun : Earth to Sun ratio be known?