# Funbers 28, 29 and 30

## The fun facts about numbers that you didn’t realise you’ve secretly always wanted to know…

**28** — **Twenty-eight**

28 has the infamy of being the second perfect number. This may sound like it came in second place in some kind of ‘best number competition’, but in fact a perfect number is one where all of the numbers that divide it, perfectly add up to give the number itself: 1 + 2 + 4 + 7 + 14 = 28. We first talked about perfect numbers back in Funbers 4.6692…, 5 and 6, which gives you a pretty big hint as to what the first perfect number might be…

Twenty-eight is also a triangular number. Building equilateral triangles using only dots gives rise to a sequence of numbers, each of which is called a triangular number. We start with a single dot, then we add a row of two dots below to make a total of 3, then we add a third row with three dots to give a total of 6, etc. etc. (see below for examples). For a triangle with seven rows the total number of dots will be 28. If you feeling brave, try to work out the general formula for the number of dots in a triangle with n rows.

So far I think we can say 28 is doing pretty well being both a perfect number and a triangular number, but it doesn’t stop there. Twenty-eight is also a magic number (yes, really). Magic numbers are a concept in nuclear physics which correspond to the total number of protons and neutrons required to completely fill a shell within an atom. There are seven magic numbers known so far: 2, 8, 20, 28, 50, 82, and 126 with at least another eight predicted by the theory.

**29** — **Twenty-nine**

Here’s a fun challenge for you: using the numbers 1, 2, 3, 4 only once, along with the four basic operations of addition, subtraction, multiplication and division, can you make a total of 29? What about all positive numbers less than 29?

It turns out that 29 is in fact the smallest positive number that CANNOT be made using the method described above (it’s Funbers, you should have known there was a twist). In other claims to fame, it takes Saturn just over 29 years to orbit the sun, there are 29 states in India, and 29 Knuts make one Sickle in the currency of the wizarding world of Harry Potter. The real question is how many Sickles make a Galleon?

**30** — **Thirty**

As we enter the fourth decade of Funbers, let’s look back at some of the interesting numbers we’ve met so far… 1, 4, 9, 16 — what do they all have in common? Adding up the first four square numbers gives exactly 30: 1² + 2² + 3² + 4² = 30. This property makes it a square pyramidal number or a cannonball number. The latter name comes from the fact that a square pyramid can be built from exactly 30 cannonballs — instructions below if you want to try it out for yourself, though I recommend using something lighter and easier to obtain than medieval ammunition.

If you’re lucky enough to reach 30 years of marriage, you celebrate the Pearl Wedding Anniversary where, as the name might suggest, you traditionally receive a gift of pearls, although the ‘modern’ list published by the Chicago Public Library suggests a gift of diamond instead. Either way, sign me up. There are in fact suggested gifts for most wedding anniversaries — too many for me to include them all — so here’s a selection of some of my favourites. I’ll let you figure out which is the traditional gift and which is the ‘modern’ one…

**1st** — Cotton or a clock

**3rd **— Leather or glass

**7th **— Wool or a pen and pencil set

**8th **— Salt or linens

**24th **— Opal or musical instruments

**85th **— Wine or your birthstone

**90th **— Stone or engraved marble

Finally, let’s end with the magical and mysterious date of February 30th. It of course does not occur on the Gregorian calendar, where February contains 28 days in a typical year and 29 days during a leap year, and so is often used as a sarcastic date to refer to something that will never happen or will never be done. That is, unless you happened to be living in Sweden during the year 1712. Instead of changing from the old Julian calendar to the new Gregorian calendar by skipping forward 11 days as had been done in other countries, Sweden decided to do things differently. Their plan was to omit all of the leap days from 1700 to 1740, which would in theory have the same result, just over a longer time period.

There were 11 leap years during this timeframe (1700, 1704, …, 1740) and so this approach would have indeed worked, were it not for the Great Northern War. The war began in late 1700 and lasted for over 20 years, which unfortunately caused Sweden to ‘ forget’ to omit the leap days in 1704 and 1708, leaving them on neither the Julian or Gregorian calendars. To avoid confusion (and likely further forgetfulness) they restored the old Julian calendar in 1712 with the addition of the magical day of February 30th. Which reminds me, I must let Taylor Swift know I can’t make our dinner next February 30th…

# Author

The Funbers series is written and presented by Dr Tom Crawford and is broadcast weekly on BBC radio. For more maths fun check out Tom’s website tomrocksmaths.com and follow him on Twitter, Facebook, Instagram and YouTube @tomrocksmaths.

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