24. Hugo, Ralph, Calvin and Willard

I’ve never been a snappy, smart dresser.  I haven’t got a body that looks good in clothes.  Mind you, I look a damned sight better with clothes than I do without them but I won’t go into that.  Even when I try to make a real effort and wear a suit, collar and tie, I still look scruffy. 

Someone told me once that I was “comfortable” in my clothes and I am not sure whether she meant as a compliment or not.  I suspect it wasn’t.  It was probably a good example of damning with feint praise.

Last October Caroline and I went to the UK.  She asked me what clothes I intended to wear while there.  She pointed out that as the only clothes I possessed were T-shirts, shorts and the suit I got married in which was then, since I had lost more than 40 lbs in weight, too big for me, I had to buy some more. 

I knew deep down that she had a point and was probably right but I argued long and hard against spending money on clothes that I would wear for two weeks and then not wear again for perhaps two years. I did a clothes inventory to assess the position:

Shoes	3 pairs (2 pairs of sandals. 1 rubber Crocs)
Socks	0
Shorts	5 pairs
Long trousers	1 pair (worn twice a week at the school I help at)
Jeans	1 pair (last worn in October 2005)
Belt	1 never used
Pants/Boxers	15 pairs
T-shirts	14
Ties	0
Sweaters/Jumpers	0
Jackets	0
Overcoats	0
Swimming trunks	4
Waterproof “System”	1 previously only worn in the Lake District

That’s all I need living here in the tropics and so, in the end, I gave up.  I could see that I was not really fully equipped for England in October and because Caroline doesn't trust me to buy clothes on my own she insisted on coming with me to buy some.  It was like going shopping with my Mum except that we didn’t end up having a sticky bun in British Home Stores afterwards.

I was led to what I was told is Cayman's premier men’s clothes shop where I was quickly taken under the caring wing of Willard, the sales assistant.  Willard seemed to be practising for the day when the BBC decides to make a remake of, "Are You Being Served."   After twenty minutes (by this time we were really close friends) he was telling me all sorts of things about his private and personal life that I really didn’t want to know.

I always work on the principle that if you don’t know anything about what you want, go for the top of the range.  This philosophy has served me well with fridges, telephones and ballpoint pens.  Not so well with cars and women but that’s a different and much longer story.  I told Willard I wanted a suit that I could wear in the UK and in Cayman.

Willard shrieked with excitement. “Hugo Boss,” he screamed.  This meant nothing to me but Caroline, who knows about these things, told me that it was a ‘NAME’.  I tried on a Hugo Boss linen suit and got a nod of approval.

 “Shirts,” said Willard, “You can’t wear a T-shirt under that.”  He produced four Hugo Boss polo shirts. Caroline liked them all and so I said yes to them all.

 Willard then informed me that I couldn’t possibly wear the suit all day and so he recommended strongly that I buy a Ralph Lauren jacket for daywear that he just knew would suit me.  I had almost lost the will to live by this point.  My wife and Willard are a formidable team.  I said yes to the jacket and yes to some socks but NO to Calvin Klein boxer shorts.  No ‘NAME’ is better than M&S.           

Caroline & Willard	9
Terry	1

That was the final score.  Three days later I was buying a case of non-alcoholic lager.  I paid using my Nationwide debit card.  It was refused.  When I got home I rang Nationwide in the UK and was put through to the Fraud Department.

 “Yes Mr Wilton,” they said.  “We’ve put a block on that card because of recent unusual activity.”

“Have you been buying clothes sir?

Afterword

We landed at Heathrow on Sunday September 30^th.  Two days later, on Tuesday, I was admitted to York hospital Intensive Care Unit and I was there for 17 days.  We flew back two days after I was released.  Of the 78 different people I had made firm arrangements to meet, I saw 11. 

I wore two of the shirts and I wore the jacket once.  I have never worn the suit and probably never will now that my waistline has expanded by more than three inches as I have fully recovered my health and eaten like a horse for the last few months.  I have put back more than thirty- five pounds of the weight that I lost.

23. 6H and Fibonacci

6H were doing number sequences a few weeks ago and they all enjoyed it immensely. Then Miss Hunte played her usual trick of telling the class, without any warning or discussion with me that, as she had to leave the room for a few minutes, “Mr Terry will talk to you.”

If anyone from a university education department is reading this, may I suggest that delivering a lesson, ‘off the cuff’ should be a requisite of any teacher-training course?  I based a whole career on it.  The very first time I was seen by an OFSTED inspector, he came up to me, as I was about to begin the lesson and asked me where my lesson plan was.

“Up ’ere mate,” I said, tapping my temple.

I decided to introduce 6H to the beauty that is the Fibonacci Sequence.  In case you don’t know it, it begins: 0, 1 and every subsequent number is the sum of the previous two numbers.  So, it goes,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……………. 

There is a formula to work out, say the 46th number in the sequence but it is much too complicated for here.  In case you’re interested, and I know you are, I’ve just worked out the 46th number and it is: 18363111903.  The 146th number in the sequence has 31 digits and that took me nearly five minutes to calculate!  It really won’t add anything for me to reproduce it, so I won’t.

I told 6H about how it occurs in nature.  Any Fibonacci number divided by the preceding number, after the first few, gives 1.618 … an irrational number.  The ratio 1:1.618 is known as the ‘Golden Ratio’.  Rectangles with length and width in this ratio are called ‘Golden Rectangles’. They are the most pleasing rectangles to the eye and their co-ordinates are used in many renaissance paintings.  

The golden ratio occurs naturally in the spiral of sunflower seeds and the coils of snail and nautilus shells.  I constructed a coil on the whiteboard using squares 1,1; 1,1; 2,2; 3,3; 5,5; 8,8 and they saw and understood how the spiral developed.  You’ve really got to see it to understand it.

Fibonacci, from Pisa, lived in the 13^th century.  He did not discover the golden ratio.  Indian mathematicians and the Egyptians knew of it several thousand years earlier.  The Great Pyramid of Gisa was built utilising it in places and The Parthenon was built incorporating it in many aspects and dimensions.   It occurs in the Mona Lisa and often in parts of The Last Supper by da Vinci.  It is aesthetically pleasing to the eye.

The length of the average human forearm to the length of the hand is 1.618 as is the length of the human face to its width.  I’ve been studying old school photographs of rugby teams and found that David’s is 1.284.  (Shrek’s is 1.262)   

Also in the human body, the ratio of the width of mouth to the width of nose is in the golden ratio, as is the ratio of the distance between the navel and knee to the distance between the knee and the end of the foot.  The same sequence can be seen in the leaves of poplar, cherry, apple, plum and oak trees.  

Interestingly (in my opinion though not in Caroline’s), paper sizes are not, ’golden rectangles’.  The ‘A’ series are in the ratio of 1 : √2.  This allows for a sheet to be folded over and over without changing the ratio.  That can’t be done with a Golden Rectangle.

6H loved it.  Then I made a bit of a mistake.  I forgot for a moment that I was talking to 10-year olds and started to tell them about the two rabbits in a field. 

Imagine a field with no rabbits in it. (0)  Into that field after one month is put one pair of newborn baby rabbits (0, 1).  We are counting the number of pairs of rabbits in the field after every month.Rabbits become sexually mature at the age of two months. 

“No, they don’t,” interrupted Rozzard.  I ignored him.  

So, after another month, there is still just one pair in the field (0, 1, 1).  One month after that, the female rabbit, now mature, gives birth to one pair, one male and one female and so now there are two pairs (0,1,1,2). 

This is when the trouble started: “My rabbit had eight babies.  They wouldn’t just have two.”  

Another month passes and the original female gives birth to another pair, one male and one female making three pairs (0, 1, 1, 2, 3). After yet another month the first female to be born is mature and she too gives birth to a pair, one male and one female; but so, does the original female and so now there are five pairs in the field (0, 1, 1, 2, 3, 5).

“That’s disgusting!   That means the father is their mother’s brother,” said Anique.

“Or their grandfather,” added Rozzard helpfully.

I’d lost them and so I set them homework.  I don’t really agree with setting homework for primary age children.  I think that at that age they should be out, doing things but I set it to use up some time until Ms Hunte returned.

“Make up a number sequence of at least five numbers, either arithmetic or geometric and I’ll work out the next two numbers in the sequence.  There’ll be a prize for anyone who beats me.”

The next time I went back they handed me their homework. Most of them were easy to work out. 1, 2, 4, 7, 11, ____  was typical and I did them all.  One of them stumped me.  It was Rozzard’s.

This was it:   6, 12,  48, 768,  196608, _____

I studied it for several minutes totally neglecting other things.  I was not going to be beaten by Rozzard.  It was clearly not an arithmetic sequence but I couldn’t see any apparent logical progression.  

“Are you sure that this works Rozzard,” I asked him and then I had a thought.  “They’re not just random numbers, are they?”

He was very indignant.  “Miss Hunte checked it,” he said grumpily. 

Miss Hunte grinned and nodded. She was enjoying my frustration as much as Rozzard.

At last I got it.  “Sorry Rozzard, no prize for you,” I said.  “6 x 2 = 12.  12 x 2 squared (4) = 48.  48 x 4 squared (16) = 768.  768 x 16 squared (256) = 196608 and so 196608 x 256 squared (65536) is 12 884 901 888. Is that the answer?” 

He wasn’t happy.  “Yes,” he grumped, “but you got it the wrong way so I still should get a prize.”

I couldn’t devote any more time to it then as I had standards to raise.  I brought it home and worked on it during the afternoon and cracked it, I think. Rozzard is going to be upset when I next see him if I’ve done it his way, because Ms Hunte told him that my prize was to be a trip to Disney World in Orlando. 

This is how Rozzard did it: 

6, 12, 48, 768, 196608, ____________

6² = 36 and 36 ÷ 3 = 12

12² = 144 and 144 ÷ 3 = 48

48² = 2304 and 2304 ÷ 3 = 768

768² = 589824 and 589824 ÷ 3 = 196608

196608² = 38654705664 and 38654705664 ÷ 3 = 12884901888

and so, that is the next number in the sequence.

Fibonacci 146 = 1454489111232772683678306641953

31 digits, so don't bother counting them!

This is a photo of us last Thursday.  I’m going to miss them all very much. 

22. Kangaroos and Oranges

As I have written before, I work, unpaid, as a classroom assistant in our local primary school. The children in the school are aged from five to eleven and are very different from the 11 – 19-year-olds that I used to teach in London.  The children in the class that I assist are aged 10 and 11.

One morning I was met by a substitute teacher as Ms Hunte, the class teacher, was away on a course.  I introduced myself and explained what kind of thing I normally did.  The woman, Ms Devonne, started working with the class and seemed to me to be doing a pretty good job.  After about half an hour she needed to set up a projector and was having some difficulty.  She needed time to sort it out and used her creative skills to make time.

“Mr Terry will talk to you,” she announced.

I was put on the spot – again!  (Different teacher, same technique)

Some mathematical facts and oddities can be the basis for a diversion needed at a time like this.

I decided to put on a show:

Me                 

Who would like to be astounded?

Class 6H       They’re not streamed.  H stands for Hunte, their class teacher.

Me, me, me, me, me …………………

Me     

I will be astounded if anyone can tell me what astounded means.

Chander       

It means, amazed or astonished, Mr Terry.

Me     

You’re right and now I’m surprised and flabbergasted. I’m shocked and dumbfounded but not surprisingly, speechless.

I needed to distract them so I asked them to write down as many adjectives that they could think of beginning with the letter ‘S’.  While they had their heads down, I went and wrote on the back of the whiteboard. The class couldn’t see what I was doing and when a boy asked what I was doing, I told him I was having a pee.

Incidentally, I could be in trouble because of that.  Caroline warned me that Cayman kids are unlikely to have never met anyone like me before and that they always believe every word the teacher tells them. They are endearingly innocent and naïve and the concepts of irony, sarcasm and taking the piss are completely unknown to them. After 35 years of teaching in London, it is wonderfully refreshing.

I checked once more and 6H confirmed that they were more than prepared to be astounded and some of them were very eager to be amazed too.

Chander confided to me that she didn’t think they could be ready to be both ‘astounded’ and ‘amazed’ as they are synonyms.  I thanked her and then, with a theatrical flourish I addressed Ms Devonne.

Me     

Don’t tell me what it is but think of any number that you are sure you can multiply by 9.

Then, looking at 25 eager faces,

You lot - do the same.  Think of a number and multiply it by 9.  Make sure you’re right by checking it with the multiplication table on the wall.

(They probably didn’t need to check because they are all very good at their times tables.  They learn them by rote and chanting one or two aloud, at least once every day. 

In my opinion, rote learning is always effective.  It does not lead to understanding, but facts are learnt.  9 x 7 = 63 is a fact.  The understanding of how and why nine sevens are sixty-three is unimportant and unnecessary for everyday life.)

OK, you have multiplied that number by 9. Your answer will either have one, two or maybe three digits in it. If it has two or three digits, add them together and find the total.

OK? Everyone ready? …… Now take away 5 from that total.

When all the preparations were complete, I spoke to Ms Devonne again.

Me     

Ms Devonne, If, 1 equals A, 2 equals B, 3 equals C and so on, work out the letter that matches your number. Then think of a country that begins with that letter.

Done that?  OK.

Now take the last letter of the country and think of an animal that begins with that letter.

Right, now take the last letter of the animal and think of a fruit that starts with that letter.

Addressing the class,

I will say a sentence and every time I pause I will point at Ms Devonne and she will fill in the missing word.

This is what happened:

“Yesterday while visiting a zoo in FRANCE, I saw an ELEPHANT eating a TOMATO”

She looked perplexed. The class didn’t look astounded and nobody looked very amazed. I probably looked embarrassed.

I was desperate to try and salvage something.

Me     

Did anyone get anything different?

Some of the children put up their hands and I pointed at Chander. Expecting the worst, I asked her what she got.

“DENMARK, KANGAROO and ORANGE,” she said.

There were a few gasps of amazement from the other kids.  Feeling very relieved and almost euphoric, I swung the board around and then there were genuine gasps of astonishment because on it I had written:

Yesterday, while visiting a zoo in DENMARK,

I saw a KANGAROO eating an ORANGE

The children were so excited because I had done what I had said I would do – I had astounded them.

Only Ms Devonne didn’t look too impressed. Then Chander ruined it all. 

“What number did you think of Ma’am?” she asked.

“I can’t remember.” 

“You must be able to,” insisted Chandra.  “What was it? I thought of eight.”

When the children had gone to lunch, a puzzled Ms Devonne told me that she couldn’t see why it had gone wrong for her.

“What number did you think of?” I asked.

“Seven,” she said.

“What are seven nines?”

“Fifty-six,” she said.

--------------------------------------

This is why it should usually work:

Any number multiplied by 9 = z, and the digits of z added together will come to 9, eventually.

So, for example:

 1 x 9 = 9       

3 x 9 = 27                                                   2 + 7 = 9       

53 x 9 = 477                    4 + 7 + 7 = 18     1 + 8 = 9       

723496 X 9 = 6511464    6 + 5 + 1 + 1 + 4 + 6 + 4 = 27         

                                                                    2 + 7 = 9

And 9 – 5 is 4

So:  if 1 = A, 2 = B, 3 = C, then 4 is ALWAYS ‘D’.

Apparently, 98% of people, when asked to think of a country beginning with ‘D’ think of Denmark.

Virtually everyone then thinks of Kangaroo. If someone buggers it up by saying, “Koala,” tell him or her that the Latin name is koaloo eucalypto. It’s not but they won’t know that unless it’s Chander.

Orange is the only fruit most people can think of beginning with an ‘O’

When I tried it out on Caroline she came up with, “a Camel eating an apple in Dominica. Perhaps it’s because of where we live in the Caribbean.