Numbers appear all the time in our lives, and I wanted to use this blog to illustrate how they appear in my daily life and in the wider world.
I have come away in the caravan with my husband for a break. The caravan hasn’t been used for over two years due to the COVID pandemic and we have really missed our trips away.
Yesterday evening we met friends for dinner. She is a surgeon and the conversation naturally turned towards medical topics. For some reason my friend mentioned that there are 206 bones in the typical human body. I had never thought about this before and, if I had, I’d have guessed a number much smaller than 206.
The Human Skeleton
Not everyone has 206 bones. Babies are born with over 300 bones and some people are born with extra bones, such as a 13th pair of ribs or an extra finger or toe.
I didn’t want to produce a list of all 206 bones but have divided them into four sets as shown in the table below – the skull, the torso, the arms and the legs.
| Area of the body | Number of bones |
|---|---|
| Skull | 28 |
| Torso | 52 |
| Arm / hand (32 x 2) | 64 |
| Leg / foot (31 x 2) | 62 |
| Total | 206 |
My thoughts about the number 206 took me further afield.
Countries Recognised by the International Olympic Committee
Interestingly, the number 206 is associated with the Olympics. The International Olympic Committee (IOC) recognise 206 countries – that is, each of these countries has a National Olympic Committee that is recognised by the IOC. Delegates from 205 teams participated in this year’s Olympics in Tokyo: North Korea did not participate due to concerns about COVID.
The United Nations (UN) recognise 193 countries (of which one is North Korea) and so there are 13 more teams than there are countries officially recognised by the UN. Since 1996 the IOC only approve internationally recognised states and the corresponding National Olympic Committees are expected to represent “an independent state recognised by the international community.” Of the 13 teams that are not UN recognised countries, four are geo-politically fraught areas:
Palestine, Hong Kong, Kosovo and Taiwan
The other nine of the teams are island regions that are all territories of, or linked to, nations recognised by the UN, but still participate separately at the Olympics:
American Samoa, Aruba, Bermuda, Cayman Islands, Cook Islands, Guam, Puerto Rico, British Virgin Islands and US Virgin Islands
To summarise:
| Countries recognised by the UN | 193 |
| North Korea did not attend | -1 |
| Geo-politically fraught areas | 4 |
| Island regions | 9 |
| Teams participating in Tokyo Olympics | 205 |
The number 206 has two properties that I found worth noting.
Untouchable Numbers
Something that I’d never heard of: 206 is an untouchable number. This means that its English name – two hundred and six – includes all five vowels exactly once:
two hundred and six
And 206 is the smallest of such numbers – the others sharing this property being 230, 250, 260, 602, 640, 5000, 8000, 9000, 80,000 and 90,000.
Consecutive Numbers with Equal Divisor Sums
A mathematical property I would never have thought about: 206 and 207 form the second pair of consecutive numbers (after 14 and 15) whose sums of divisors are equal as illustrated below:
The number 14 is divisible by 1, 2, 7 and 14
1+2+7+14=24
The number 15 is divisible by 1, 3, 5 and 15
1+3+5+15=24
From the above you can see that both 14 and 15 have a sum of divisors of 24.
Similarly, for consecutive numbers 206 and 207:
The number 206 is divisible by 1, 2, 103, 206
1+2+103+206=312
The number 207 is divisible by 1, 3, 9, 23, 69, 207
1+3+9+23+69+207=312
Thus, from the above, you can see that 206 and 207 have a sum of divisors of 312.
Last Thought
I love the way that a discussion over dinner can lead me to think about the human anatomy, the Olympics together with more general properties of numbers. In this blog I will use numbers to take you on many similar adventures!