A recap of some of the fundamental parts of a circle, including some that are easy to forget:

Diameter — a line crossing the circle through its centre. Also the longest straight line you can draw in a circle.

Radius — a line from the centre to any point on the edge. Also, half the diameter.

Sector — the classic Trivial Pursuit cheese, pizza or cake slice formed by two radii.

Area — equal to pi x the radius squared.

Circumference — equal to pi x the diameter.

Chord — a straight line touching any two points of a circle. The longest chord is the diameter.

Segment — the areas on either side of a chord, major and minor.

Tangent — a straight line just touching the edge of the circle without crossing it. It forms a right angle to the radius on the edge. Just as if you were able to lean a ladder against one.

More maths and science refreshers: States of matter, BODMAS (or PEMDAS), the 9 times table on your fingers, binary, incidence and reflection

Parts of a circle

School mathematics refresher: when faced with a calculation that looks like it could be tackled multiple ways, use BODMAS to help clear it up (See PEMDAS at the end).

BODMAS is an acronym (as opposed to an initialism) that tells you the order of operations to tackle in a calculation.

BODMAS stands for Brackets, Order/Indices, Division, Multiplication, Addition, and Subtraction. So in 2 + 4 x 2 you don't end up with 6 x 2 = 12 but instead, 2 + 8 = 10

BODMAS is generally built into calculators (you can search 2 + 4 x 2 in Google to see). If you need additions or subtractions to be carried out first you can surround them in brackets eg (2 + 4) x 2

I always learned it as BODMAS, but many people told me they learned this as PEMDAS. The idea is the same just the words are different, and the ordering of Division and Multiplication, which are interchangeable:

PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction

BODMAS

We find it handy to count in the decimal system using 10 numbers from 0,9, known as base 10, before we have to put two together to make 10 to keep counting further — 10 fingers and toes and all. But it turns out you can represent all numbers equally using just two digits, known as base 2, a 0 and a 1. This is called the binary system and is credited to Gottfried Wilhelm Liebniz in the 1600s.

The binary system is handy because 1s and 0s can be represented by simply by on/off and reproduced in as simple means as pebbles in trays , the sign of a magnetic field eg positive/negative, or a gate as open or closed. This made them the choice for designing computers and is how digital information is stored and transmitted today.

When we write a decimal number we use positional notation with each successive position representing 10 to the next power. So 739 is understood as (7 x 10^2) + (3 x 10^1) + (9 x 10^0). 10 to the power 2 is 10 x 10, so is the number of 100s in the number. Anything to the power 0 is 1.

The same is true in binary, so 1101 is understood in decimal as:

1101 = (1 x 2^3) + (1 x 2^2) + (0 x 2^1) + (1 x 2^0)

1101 = (1 x 8) + (1 x 4) + (0 x 2) + (1 x 1)
     = 8 + 4 + 0 + 1
     = 13

Each 0 or 1 in a binary number is known as a bit — named by Claude Shannon as short for binary digit — and 8 bits is known as a byte.

Translating to decimal looks fiddly, but computers don't have to do that, they can just add, subtract or multiply the binary numbers directly. Amazing to think that the device you may be reading this on now is just incredibly efficient at manipulating 1s and 0s.

For a readable and visual introduction to the history and operation of computers — from binary, logic gates, transistors, circuits, and Moore's law through to software and AI — you could do a lot worse than my Dad's book The Computing Universe 😀

Binary

A school science refresher: the 3 primary states of matter, solids, liquids and gases and the transitions between each one. If you’re like me you probably forget about the more obscure sublimation and deposition directly between solids and gases. And vaporisation of a liquid is evaporation, occurring at the surface, if it is below boiling point, otherwise it’s boiling.

There are some more unusual states including plasma — seen in lightning and fluorescent lights — and Bose-Einstein condensates, but mostly we’re familiar with ice cubes, water and steam.

States of matter

You may remember this little trick from school. If you’ve not seen it before, give it a quick try 🙂

Refresher sketches