# How big are pizzas?

Is a 12-inch pizza twice as big as a 6-inch pizza?

Simply put, no. The amount of pizza (its area) is proportional to the square of its diameter, so a 12-inch pizza is actually four times bigger than a 6-inch one.

Looking at the cost per square inch shows an interesting pattern: as size increases, the cost per square inch goes down. (Data from Dominos Pizza.)

If we take the trend that the data is following and solve the equation of the trendline (line of best fit) then we find two possible solutions: the cost per square inch falls to £0.00 at a diameter of either −128 inches or 22 inches. Since a pizza with a diameter of negative 128 inches is clearly ridiculous, it’s the free 22-inch pizza that is interesting.

# Shapes of equal width

Circular objects roll because a circle is a shape of equal width. No matter where you measure from, the distance from one side to the other (through the centre) is the same. But circles aren’t the only shape with this property.

Two British coins are shapes of equal width: the 20p (21.4 mm) and 50p (27.3 mm) coin. Having an equal width makes the coins able to roll and prevents them from getting stuck in machinery. Shapes of equal width also make good manhole covers; because no “side” is any shorter than any other, it is impossible for the cover to fall down the manhole. Circles are easiest to make which is why most manhole covers are circular.

# Ebb and Flow

The twin Gravity Recovery And Interior Laboratory satellites were initally given the highly original names of GRAIL-A and GRAIL-B. But thanks to students at a Montana elementary school they are now the best-named satellites out there.

I can’t think of better names for twin satellites designed to map gravitational fields.

# The polarisation of the sky

When light from the Sun or the Moon strikes Earth’s atmosphere it is scattered, sent in all directions by the atoms and molecules that make up the air. During this scattering process some of the light is polarised – instead of the electric and magnetic fields oscillating in many planes simultaneously, they oscillate in only one plane.

The polarisation of the light from the Sun or Moon is at right angles to the direction that the light is coming from; when the Sun or the Moon is very low in the sky (at sunset/sunrise or moonset/moonrise) the direction of polarisation is parallel to the horizon. The degree of polarisation depends on the angle between the light and the atmosphere, with the greatest degree of polarisation occuring when looking at 90° to the source.

Source: Christopher Kyba

The image on the left shows the degree of polarisation observed in a rural location. The image on the right shows the same section of the night sky, but observed from an urban location (the circular patterns in both images are caused by the movement of stars across the sky.) Because light pollution from streetlamps is not polarised, the effect of the streetlamps is to destroy the polarisation “data” that some animals use to navigate.

Source: C. C. M. Kyba, T. Ruhtz, J. Fischer and F. Hölker “Lunar skylight polarization signal polluted by urban lighting”, Journal of Geophysical Research 116 (2011). doi: 10.1029/2011JD016698.

# Whiteboards

Sometimes after a lesson I take a photograph of the whiteboard left over. Some recent photographs are below.