Welcome to my little slice of cyberspace.
Paintings of people, places and things.

Also, Ponderings about things that are probably pointless.....
yet may help you amuse yourself.
Particulary if the internet, god# forbid, is not available.
(#your choice)

Selected Work

A selection to give a flavour of my work.
More are available to view in the gallery section should these whet your appetites

Big Sky - Nine Muses and the Wave

Margate Sky

Imagine - John at Leadenhall

We Walked On

Seven Sisters

The Ghost of Christopher Robin

Ponders

  1. 1. PI Memorisation to 1000 places
  2. 2. Mental squaring three digit numbers

PI MEMORISATION TO 1000 PLACES

Background

There are many people out there that can do this – to a greater or lesser degree – but, many many years ago (i.e. my youth), I set myself the task of memorizing the irrational (i.e. random / non-repeating) number of Pi to 1000 places. This I did, and I now want to share my method to anyone who’s interested. Of course, in the world of Pi memorisers since then, my achievement has become less and less and less significant as there now some truly incredible achievements, running into may tens of thousands, on record. For myself I stopped at a thousand because a) it seemed like a good place to stop and b) it seemed like good place to stop. I have only ever used it to ramble through it from time to time as a mental workout – at my increasing age (64 this year) it is quite useful as an indicator i.e. failure = little grey cells leaving the building. Please to report still alright so far. I’m nothing special – I can do this – so can you!

Method

I use a home grown two layered alphabetic index ‘key’ based on the Major system, which itself has been around for many hundreds of years. I’ve no intention of explaining the Major system outside of suggesting you click on the following three word link Major System - Wiki (and just read the first part). The major system 1=T/D 2=N 3=M 4=R 5=L 6=SH/CH/Z/J 7=G/CK/K 8=V/F/Ph 9=P/B 0=S forms the second part of my index and my hand selected alphabetic progression of A B C D E S G H N O forms the first. So, from this are constructed 100 index keys which logically follow the sequence AT, AN, AM, AR, AL, ACH, AG, AV, AP,AS, BT, BN, BM, BR…….. all the way to …. OF, OP, OS

Please keep reading – almost there.

We now split the first 1000 digits of Pi into 100 strings of 10 digits each and then put the index at the front. So, to keep things simple, I'll demonstrate with the first 30 decimal digits 141592653589793238462643383279 like so:
AT1415926535
AN8979323846
AM2643383279
Now any type of sentences can be constructed for each block adhering to the rule of a) using the index in the first word and b) using the 10 numbers that follow to construct any sentence - however nonsensical - that fits with the major system.The whole underlying principle here is that 100 sentences are all you need to store in your memory bank to memorise 1000 digits of Pi. Sentences can easily be stored and retrieved, and give a visual and conceptual form to an otherwise soulless number string. Use your imagination! Some examples for you are:
ATe TuRTLe Pie a NiGeLla MeaL
ANy PhoBiC PieMaN May FoRGe
AMy eNSuRe Me My FoaMiNG Pie

Please note that in a double letter situation e.g. Nigella, only the first 'L' will be significant.

What is the purpose of the index I hear you ask? Well a) to help you effortlessly keep the blocks of 10 in correct sequence (because they follow a logical order) and b) as a doorway – what I mean is once you have constructed your own personal hundred sentences, and practised a bit, you only need to recall the index, and the rest of your sentence should follow naturally. Eventually you get to the point where, not only do you not need to recall the sentence itself, you can use the index sequencing to help quickly answer such questions as “what is the xxxth digit of Pi”. You can even recite the whole thing  backwards! Hope you have fun with this – it's press ups for the brain. I also hope I have explained it well enough - let me know if you have any queries on the subject.


MENTALLY SQUARING 3 DIGIT NUMBERS


Background

Mentally squaring 3 digit numbers requires knowing a small set of different component strategies for whole or partial numbers and recognising when to apply them.
What follows stems entirely from quadractic theory, but there is none of that nitty gritty here: the intention is to present an approach that can be pictured in the mind and flows as a sort of current rather than trying to write blindfold on a blackboard pictured in your head!

Here are the individual components:

A. Two digit numbers near 50
Any such number can be quickly squared by subtracting 25 from it, imagining 00 on the end, and adding to this the two digit square of the difference between that number and 50. Again, sounds awful - seeing examples is much easier:

53 squared = 2809 [53 minus 25 = 28, and 53 - 50 = 3. So square the 3 and add 09 on the end of 2800]

39 squared = 1521 [39 minus 25 = 14, and 50 - 39 = 11. So square the 11 and add 121 on the end of 1400]

B. Numbers ending in five

Any mumber ending in 5 can be squared by multiplying the number / all numbers before the 5 by that number plus itself plus one and sticking 25 on the end. Confused? here's 2 examples to show how simple it is:

35 squared = 1225. [3 times (3 + 1) with 25 stuck on the end i.e. 3 times 4 = 12 with 25 stuck on the end]

135 squared = 18225 [13 times (13 + 1) with 25 stuck on the end i.e. 13 times 14 = 182 with 25 stuck on the end]


C. Numbers approaching base 10 limits (10, 100 1000 etc)
A slight variation on B. In words, double the number, take away 100 and then imagine 00 on the end of the result. To this add the square of the difference between the original number and 100. Much easier to see!

87 squared = 7569 [87 doubled is 174. Take away 100 and imagine 00 on the end is 7400. To this add 100 - 87 (which is 13) squared, so adding 169 to 7400 ]

93 squared = 8649 [93 doubled is 186. Take away 100 and imagine 00 on the end is 8600. To this add 100 - 93 (which is 7) squared, so adding 49 to 8600]


Putting it all together

When confronted by a three digit number my first thought is 'how does this break down something ending in 50 and what's left?

Examples:

371 squared is (350 plus 21) squared, in other words, this is (350 squared) plus ((350 plus 350) times 21) plus 21 squared. Summary: 1225 plus (7 times 21) with two 0's on the end, being 137200, to which I add 441. Answer = 137641

838 squared is (850 minus 12) squared, in other words, this is (850 squared) minus ((850 plus 850) times 12) plus 21 squared. Summary: 7225 minus (17 times 12) with two 0's on the end, being 702100, to which I add 144. Answer = 702244

982 squared is (982 times 2) minus 1000 to give 864 and imagine 000 on the end to give 864000. To this add (1000 minus 982) which is 18, that is squared to 324 and added. Answer = 864324.


Last Comments

The only other variation to mention is when a three digit number is just above a base 10 break. For instance 103, or 407. In these cases, all that is needed is to double the last two digits, then multiply the result by the hundred digit. To this is added the square of the original last two digits.... as ever, easier to see.

103 beomes 103 + 3 = 106. Multiplying 106 by 100 gives 10600, to which is added 3 squared giving the answer 10609.

407 becomes 407 + 7 = 414. Multiplying 414 by 400 gives 165600, to which is added 7 squared giving the answer 165649.


There are other strategies, for 3 as well as 4 and 5 digit numbers - but this is probably more than enough to be going on with now!
Happy squaring

News

  1. Update 27 July 2107: Exhibition 2018 News: new work
  2. Update 26 June 2107: Exhibition 2018 News: new work
  3. Update 20 June 2107: Exhibition News for 2018
  4. Update 26 April 2017: Not The Royal Academy
  5. Update 4 April 2017: New Site

New Painting: 27 July 17:
New work for the Exhibition next April. It is oil on canvas (12 by 10 inches) and titled ' Pondering at Ellison's Pond', located at Ellison's Pond on Ashdown Forest. It is a little bear quietly pondering some of life's larger questions --- for absolutely no reason at all.
This, and all other new work, will show on the Gallery page

I'm back in full production now, and need to be to keep up with co- exhibitor Maggie Tuite!

Pondering at Ellison's Pond


New Painting 26 June 17:
This new work is a miniature - in oil on canvas measuring 5 by 7 inches. It provided a good test of the eight screws and metal plate now holding my painting wrist together!

Walking at Wren's Nest

It shows a couple walking at Wren's Nest on Ashdown Forest - one of my favourite places, and will show at next year's Exhibition at the Forest Centre.
More works will posted as they leap off the easel...... keep an eye here or on Facebook.


Exhibition News 2018
I am very pleased to be exhibiting some new work in 2018 at the Ashdown Forest Centre Gallery from April to June.
I am even more pleased that this will be a joint exhibition with the fabulous textile artist Maggie Tuite. For those of you unacquainted with her wonderful creations, cruise on over on the link to her facebook site here and bask in the fantastic colours she makes come alive!
Our work will be for sale as originals, and in some cases also as limited runs of top quality colour, permanant giclee prints.
My intention is to update this site with my show pieces as they complete. Keep an eye on Maggie's! More later................

Not The Royal Academy:
John Lennon at Leadenhall is to be exhibited in the famous Not The Royal Academy exhibition at the London Lewellyn Gallery in June this year.
Well worth a visit my friends.......... particularly for buying a painting featuring John Lennon ;)

Imagine - John at Leadenhall

The link below takes you to the exhibition website:


New Site:
Discovered the wonderful people at HTML5 UP and am busy tweaking one of their designs for a new site. Thanks people!