I mentioned perfect numbers yesterday. There are also amicable numbers which are a bit like perfect numbers but are in pairs. The smallest pair is 220 and 284.
The divisors of 220 are 1,2,4,5,10,11,20,22,44, 55 and 110 which total 284.
The divisors of 284 are 1,2,4,71 and 142 which total 220.
nigt EL slim, moonsiee
Besides perfect numbers and amicable numbers there are also sociable numbers. Same concept other than there's more than two in the sequence of numbers before getting back to the first number. For instance there's a 5 number sequence which starts with 14,296 which leads to 14288, 15472, 14536, 14264 and back to 14,296. The longest sequence found is of 28 numbers.
The vast majority of numbers just result in getting to 1. For instance:
100 - 1,2,4,5,10,20,25,50 totals 117
117 - 1,3,9,13,39 totals 65
65 - 1,5,13 totals 19
19 is a prime number so the only divisor is 1
@El Loro posted:Besides perfect numbers and amicable numbers there are also sociable numbers. Same concept other than there's more than two in the sequence of numbers before getting back to the first number. For instance there's a 5 number sequence which starts with 14,296 which leads to 14288, 15472, 14536, 14264 and back to 14,296. The longest sequence found is of 28 numbers.
The vast majority of numbers just result in getting to 1. For instance:
100 - 1,2,4,5,10,20,25,50 totals 117
117 - 1,3,9,13,39 totals 65
65 - 1,5,13 totals 19
19 is a prime number so the only divisor is 1
Iâm confused El 
@Moonie posted:Iâm confused El
My post was about divisors of numbers. Using 100 as an example, the only numbers which 100 can be divided by (with nothing left) are 1,2,4,10,20,25 and 50.
It's only of any interest to people who have any interested in numbers and puzzles.There was a maths thread a few years ago to which some of us posted on.
@El Loro posted:
It's only of any interest to people who have any interested in numbers and puzzles.There was a maths thread a few years ago to which some of us posted on.
That bit I understand 
Decades ago when I was doing my maths O level our teacher gave us a trigonometry poser. Take any triangle. For each angle split the angle into three equal angle drawing straight lines. For each side, two of the nearer lines will meet at a point. So there will be three meeting points. Draw straight lines for the three point to form a small triangle.
The poser is to prove that the small triangle is always an equilateral one regardless of the angles of the original triangle.
There's a wiki article on Morley's trisector theorem which includes a diagram of what I'm talking about. No point in me putting a link here as the wiki address used is one of those which doesn't work on this forum.
The diagram is fairly easy to understand but trying to prove this is one only for mathematicians.
@El Loro posted:Decades ago when I was doing my maths O level our teacher gave us a trigonometry poser. Take any triangle. For each angle split the angle into three equal angle drawing straight lines. For each side, two of the nearer lines will meet at a point. So there will be three meeting points. Draw straight lines for the three point to form a small triangle.
The poser is to prove that the small triangle is always an equilateral one regardless of the angles of the original triangle.
There's a wiki article on Morley's trisector theorem which includes a diagram of what I'm talking about. No point in me putting a link here as the wiki address used is one of those which doesn't work on this forum.
The diagram is fairly easy to understand but trying to prove this is one only for mathematicians.
Although I spent a good deal of my working life in accounts , I gave up trying trying to understand trig âĶor algebra âĶat schoolâĶ.I was useless at it .
@Baz posted:Although I spent a good deal of my working life in accounts , I gave up trying trying to understand trig âĶor algebra âĶat schoolâĶ.I was useless at it .
One of the clients I had when I was I was an audit manager was a provider of finance to other businesses. The client had lots of subsidiaries with a variety of year ends. One year they changed their accounting system during the course of the year. Then the group year end came. All the subsidiaries had to to accounts to that year end besides their own year end. It was at that point in time when the client discovered that due to the change of the accounting system, the subsidiaries were unable to generate the figures necessary to get accounts for the group year end. Their own year end weren't a problem.
The clients accountants tried to see if they could work out how to generate the figures needed but couldn't.
I got to hear about this one Friday afternoon. I got the client to give me some specimen reports to see if I could work out how to generate the needed figures over the weekend. I succeeded and on the following Monday morning I gave the client the way to work the figures out.
It was an algebraic formula with say a dozen variables. The only time in my accountancy career where algebra was really useful
(after I was made redundant and became self employed I would go to that client to help in their year end accounts work, I earned quite a lot of money for a few years and that was their way of thanking me for saving them)
@El Loro posted:One of the clients I had when I was I was an audit manager was a provider of finance to other businesses. The client had lots of subsidiaries with a variety of year ends. One year they changed their accounting system during the course of the year. Then the group year end came. All the subsidiaries had to to accounts to that year end besides their own year end. It was at that point in time when the client discovered that due to the change of the accounting system, the subsidiaries were unable to generate the figures necessary to get accounts for the group year end. Their own year end weren't a problem.
The clients accountants tried to see if they could work out how to generate the figures needed but couldn't.I got to hear about this one Friday afternoon. I got the client to give me some specimen reports to see if I could work out how to generate the needed figures over the weekend. I succeeded and on the following Monday morning I gave the client the way to work the figures out.
It was an algebraic formula with say a dozen variables. The only time in my accountancy career where algebra was really useful
(after I was made redundant and became self employed I would go to that client to help in their year end accounts work, I earned quite a lot of money for a few years and that was their way of thanking me for saving them)
Way to go El 
A search to see if the identity of some people can be identified from some photos taken back in the 1950/60s. The photos were taken by Bristolian photographer Herbert Shergold. So the people would probably have lived in Bristol at the time.
https://www.bbc.co.uk/news/articles/cp8mg23yv6xo
@El Loro posted:A search to see if the identity of some people can be identified from some photos taken back in the 1950/60s. The photos were taken by Bristolian photographer Herbert Shergold. So the people would probably have lived in Bristol at the time.
https://www.bbc.co.uk/news/articles/cp8mg23yv6xo
Will be interesting to see if anyone comes forwrd with information on the photographer El..
@slimfern posted:Will be interesting to see if anyone comes forwrd with information on the photographer El..
Yes, Slim
There's more photos on the Bristol Live website:
https://www.bristolpost.co.uk/...0s60s-photos-9624913
20 including those shown on the BBC site. 4 per page, buttons for each page at the end, don't use the arrow > seen on the right. The 4th one on the 4th page and the 1st on the 5th are clearly of the same person.
@El Loro posted:Yes, Slim
There's ore photos on the Bristol Live website:
https://www.bristolpost.co.uk/...0s60s-photos-9624913
20 including those shown on the BBC site. 4 per page, buttons for each page at the end, don't use the arrow > seen on the right. The 4th one on the 4th page and the 1st on the 5th are clearly of the same person.
Or as commented, they could be identical twins 
@slimfern posted:Or as commented, they could be identical twins
When my brother was at senior school he had a couple of friends who were identical twins, well almost. One of them had an eye with a different coloured iris to the other eye, whereas the other twin had eyes with the same coloured iris.
@slimfern BBC Two showing a film tomorrow afternoon at 12.15. I don't seem to have mentioned it before to you but it's likely that you have seen it before,
"The Third Man" (1949) Joseph Cotten, Trevor Howard and Orson Welles as Harry Lime,. Directed by Carol Reed. Zither music by Anton Karas.
Major classic, a must watch if you haven't seen it before.
@El Loro posted:@slimfern BBC Two showing a film tomorrow afternoon at 12.15. I don't seem to have mentioned it before to you but it's likely that you have seen it before,
"The Third Man" (1949) Joseph Cotten, Trevor Howard and Orson Welles as Harry Lime,. Directed by Carol Reed. Zither music by Anton Karas.
Major classic, a must watch if you haven't seen it before.
Thanks El...Yes I have seen it before
As you say though...a classic and always worth a watch. 
@slimfern posted:Thanks El...Yes I have seen it before
As you say though...a classic and always worth a watch.
I though it likely that you had seen "The Third Man" before, Slim
Although some have speculated that Welles was involved in directing the film, any involvement by film other than acting was probably minimal - he may have written some lines of his dialogue.
Carol Reed may have been influenced by some of Welles's films as would many other directors. However his earlier film "Odd Man Out" (1947) shows that he would not have needed any assistance from Welles. "Odd Man Out" is darker in tone than "The Third Man" and the scene where James Mason is hallucinating is quite scary. An outstanding film but dark.
@El Loro posted:I though it likely that you had seen "The Third Man" before, Slim
Although some have speculated that Welles was involved in directing the film, any involvement by film other than acting was probably minimal - he may have written some lines of his dialogue.
Carol Reed may have been influenced by some of Welles's films as would many other directors. However his earlier film "Odd Man Out" (1947) shows that he would not have needed any assistance from Welles. "Odd Man Out" is darker in tone than "The Third Man" and the scene where James Mason is hallucinating is quite scary. An outstanding film but dark.
I don't think I've watched 'Odd Man Out'...it sounds like a film I wouldn't enjoy tbh. 
@slimfern posted:I don't think I've watched 'Odd Man Out'...it sounds like a film I wouldn't enjoy tbh.
"Odd Man Out" is a very good film, Slim, but it's not one to enjoy.
Another James Mason film is on BBC Two at present - "Julius Caesar" (1953) based on Shakespeare's play. He's Brutus in that. May be a good film but not really an enjoyable one 
@El Loro posted:"Odd Man Out" is a very good film, Slim, but it's not one to enjoy.
Another James Mason film is on BBC Two at present - "Julius Caesar" (1953) based on Shakespeare's play. He's Brutus in that. May be a good film but not really an enjoyable one
No, I read the book in school...that was brutal enough
night EL slim moonsieee
Slim, I haven't spotted much new of interest to you on the Talking Pictures tv channel during the coming week,
On Tuesday afternoon is an American film adaptation of "Lorna Doone" (1951) which was filmed there rather than in Devon. The two leads were Barbara Hale (Della Street of the Perry Mason tv series) and Richard Greene (Robin Hood).
Next Sunday evening is "The Deep Blue Sea" (1955) getting a rare showing. That's Terence Rattigan's play which he adapted for this film. Kenneth More reprises the role he played in the original stage performance. Vivien Leigh played the role which was played by Peggy Ashcroft on stage. Looking at the plot, I think it unlikely you would want to watch it.
One of the best of all of the Tom and Jerry cartoons - "The Cat Concerto" (1947) which got an Oscar:
https://www.youtube.com/watch?v=-pWOlXpR_lI
It's actually Liszt's Hungarian Rhapsody No. 2.
And a performance of the Rhapsody with the cartoon in the background:
https://www.youtube.com/watch?v=E1JKd1C7izQ
There is a 1946 Bugs Bunny cartoon called "Rhapsody Rabbit" which has similarities, same music and also a mouse.
@El Loro posted:One of the best of all of the Tom and Jerry cartoons - "The Cat Concerto" (1947) which got an Oscar:
https://www.youtube.com/watch?v=-pWOlXpR_lI
It's actually Liszt's Hungarian Rhapsody No. 2.
And a performance of the Rhapsody with the cartoon in the background:
https://www.youtube.com/watch?v=E1JKd1C7izQ
There is a 1946 Bugs Bunny cartoon called "Rhapsody Rabbit" which has similarities, same music and also a mouse.
Hilarious
@El Loro posted:Slim, I haven't spotted much new of interest to you on the Talking Pictures tv channel during the coming week,
On Tuesday afternoon is an American film adaptation of "Lorna Doone" (1951) which was filmed there rather than in Devon. The two leads were Barbara Hale (Della Street of the Perry Mason tv series) and Richard Greene (Robin Hood).
Next Sunday evening is "The Deep Blue Sea" (1955) getting a rare showing. That's Terence Rattigan's play which he adapted for this film. Kenneth More reprises the role he played in the original stage performance. Vivien Leigh played the role which was played by Peggy Ashcroft on stage. Looking at the plot, I think it unlikely you would want to watch it.
Thankyou El
night EL slim moonsiiee bazzy
An extraordinary performance by Maya Kimura of J S Bach's Chaconne movement of his Partita in D minor BWV 1004, He composed it for the violin, Karl Scheit transcribed it for the guitar. She has used that transcription for her performance.
She's playing it on a Japanese instrument known as a koto which is the national instrument. This koto has 25 strings, they generally have fewer,
https://www.youtube.com/watch?v=h-tsbumcyVc
@El Loro posted:An extraordinary performance by Maya Kimura of J S Bach's Chaconne movement of his Partita in D minor BWV 1004, He composed it for the violin, Karl Scheit transcribed it for the guitar. She has used that transcription for her performance.
She's playing it on a Japanese instrument known as a koto which is the national instrument. This koto has 25 strings, they generally have fewer,
https://www.youtube.com/watch?v=h-tsbumcyVc
Amazing El
She makes it look so easy...
