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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
@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

Iโ€™m confused El

Moonie

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
Last edited by El Loro
@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 โ€ฆor algebra โ€ฆat schoolโ€ฆ.I was useless at it .

Baz
@Baz posted:

Although I spent a good deal of my working life in accounts , I gave up trying trying to understand trig โ€ฆor algebra โ€ฆat schoolโ€ฆ.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
@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

Baz
@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
@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
@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