What are you doing right now?

[TimO]

He was trying to find a lowest common denominator in order to order fractions.
4/16  2/6  3/4   1/2  6/10  and  1/8 ...

Isn't the obvious brute force approach to just multiply all of the denominators by all of the other denominators? (and obviously the numerator by the same set, minus the original denominator of that fraction).

ie you get:

4*(6*4*2*10*8)/(16*6*4*2*10*8)
2*(16*4*2*10*8)/(16*6*4*2*10*8)
3*(16*6*2*10*8)/(16*6*4*2*10*8)
1*(16*6*4*10*8)/(16*6*4*2*10*8)
6*(16*6*4*2*8)/(16*6*4*2*10*8)
1*(16*6*4*2*10)/(16*6*4*2*10*8)

15360/61440
20480/61440
46080/61440
30720/61440
36864/61440
7680/61440

Which is then trivially sortable.

[Kim]

He was trying to find a lowest common denominator in order to order fractions.
4/16  2/6  3/4   1/2  6/10  and  1/8 ...

Isn't the obvious brute force approach to just multiply all of the denominators by all of the other denominators?

Yes.  Well, it is if you're of a computer science persuasion, anyway.  I started doing that then realised it probably wasn't what the junior school maths lot would have in mind, and opted for the same sort of frustratingly non-algorithmic method that we were taught to use at A-level for integration: Staring at it for a bit, cancelling where appropriate, then pulling the answer out of thin air.

I can't help thinking that a Chinese Room approach to maths teaching would have made life a lot less complicated...

[Jurek]

Wondering where I'm going to get my post chilli-con-carne chocolate fix from

There's bugger all to be found in this household.
I cannot be asked to venture out.
And I don't feel profligate enough to have some delivered by my local mini-cab firm.
Meh!

[eck]

Excellent  .
Eck, I see a picture of someone who has discovered that they are their own person, and that they are at ease with that.

Later developments will, er, develop. 

Aw, Basil, that is so right.
Later developments? So far so good. 

[matthew]

He was trying to find a lowest common denominator in order to order fractions.
4/16  2/6  3/4   1/2  6/10  and  1/8 ...

Isn't the obvious brute force approach to just multiply all of the denominators by all of the other denominators?

Yes.  Well, it is if you're of a computer science persuasion, anyway.  I started doing that then realised it probably wasn't what the junior school maths lot would have in mind, and opted for the same sort of frustratingly non-algorithmic method that we were taught to use at A-level for integration: Staring at it for a bit, cancelling where appropriate, then pulling the answer out of thin air.

I can't help thinking that a Chinese Room approach to maths teaching would have made life a lot less complicated...

Start by simplifying the fractions 4/16 = 1/4, 2/6 = 1/3 and 6/10 = 3/5

Take all the denominators, 4, 3, 4, 2, 5, 8

set aside any that are factors of one of the others, in this case 4, and 2 to reduce the set to 3, 8, 5

Multiply out to get 120

now multiply each denominator and numerator by the required amount to get to the X/120

a)30/120, b)40/120, c)90/120, d)60/120, e)72/120 and f)15/120

reorder largest first: c) e) d) b) a) f)

translate back to original fractions:
3/4, 6/10, 1/2, 2/6, 4/16, 1/8

I admit to initially not simplifying the fractions which leads to working in X/240 and more faff.

[CrinklyLion]

He got to trying /80 very quickly, having spotted in about 2 seconds that _nearly_ all of em would work with that.  Then noticed /6 and, I suspect, thinking "I'm too tired for 6x80 and then working out the equivalents!" couldn't get past the mental block and change direction.  Had he simplified them first it would have simplified his life!

[tiermat]

Finally getting around to listing bikes and frames on eBay.

[mrcharly-YHT]

set aside any that are factors of one of the others, in this case 4, and 2 to reduce the set to 3, 8, 5

very similar to the multiplication of primes technique, but yours is simpler (since it doesn't involve finding the primes, which can be a non-trivial exercise).

Any maths-sparks here that know this?  For a given number, is there only one set of primes that produce that number when multiplied together?

I admit to initially not simplifying the fractions which leads to working in X/240 and more faff.

Ditto

[matthew]

Any maths-sparks here that know this?  For a given number, is there only one set of primes that produce that number when multiplied together?

Yes they are unique for each number and termed the prime factors e.g. 8 = 2*2*2, 12=3*2*2 or 289=17*17. Any other set of factors e.g. 12=6*2 or 4*3 is only part way there as in these cased 6 and 4 are not prime and factorising these will both lead to 2*2*3.

[mrcharly-YHT]

ty

Ain't numbers wierd?

[interzen]

ty

Ain't numbers wierd?

http://en.wikipedia.org/wiki/Surreal_number

Yes. Yes they are - what other explanation could there be for the existence of, say, surreal numbers? Not to mention things like this:




Had my A-level maths teacher not been the Spawn of Satan I could have easily ended up studying mathematics instead of theoretical physics. In particular I find number theory to be absolutely fascinating.

[matthew]

set aside any that are factors of one of the others, in this case 4, and 2 to reduce the set to 3, 8, 5

very similar to the multiplication of primes technique, but yours is simpler (since it doesn't involve finding the primes, which can be a non-trivial exercise).

Yes this is a slight short cut though, change 6/10 to 7/10 so that the fraction does not simplify and my set would become 3, 8, 10 and suggest working with 240 where we know 120 works.

There is need for an additional step to ask after excluding those numbers which are factors of another: if in the reduced list of denominators there are shared factors? In the modified case both 8 and 10 share the factor 2 which is therefore only needed once in the Lowest Common Multiple and so you can have 3*8*10 / 2 = 120.

[tiermat]

Now waiting for my music client to catch up with the fact that I have removed ALL spaces from filenames in my MP3 collection.  It is currently busy removing ~20K tracks, then will be busy adding ~20K tracks...

[jogler]

I'm scoffing jam roly poly pud & custard & thinking that I'll give up cycling & take up gratuitous scoffing as an alternative hobby

[matthew]

But do enough cycling and the scoffing isn't gratuitous, it's fuel.

Also your likely to live (and scoff) for longer. 

[Wombat]

Copying data off a friend's son's hard disk onto my little backup drive.  Said PC had got itself into a never-ending reboot loop, whatever we tried.  the disc when attached to my PC showed several bad sectors and errors, which it claimed to fix.  So, do I throw it away or try for a reformat and then rebuild his PC from scratch....

I must confess I hadn't realised that if you stick in an extra disc that has bad sectors, then Windows goes straight to chkdsk and attacks them, as soon as my PC boots up.

As is usual for a 14 year old boy, its structure is a mess.  How can he ever find anything again, its all over the place?  Said boy is more into fixing traction engines that PC's, it must be said.

Norton is now getting into the act, and is NOT PLEASED wth the disc.

[interzen]

Trying to stay awake whilst enduring (which is precisely the right word) a training course on Adobe's DPS system - I was late to bed last night, had trouble sleeping and the course material is soul-crushingly dull.

I'm stuck in said course until 5.30 (with a break for lunch) which means I'll not be able to do tonight's pub ride and hence break 1000km for the year

[bumper]

Planning a trip to Mull.

I've decided I'm not waiting for summer. I'm not taking a phone, laptop, iPad or any other form of communication. I don't want to speak to anyone for a week at least, especially anyone I know through work!

I'm just making a camping list, then I'm picking a date.

[LindaG]

Fuming impotently over Cameron's response to the Frances report.

[interzen]

Planning a trip to Mull.

Get to Oban, get ferry to Craignure, tell world+dog to get stuffed for n days. Simples

I'm considering a trip to Islay and Jura for pretty much the same reasons.

I really need to go back to Mull, though - I love the place to bits. The only downside is now that I'm teetotal the Mishnish Arms in Tobermory loses a lot of its appeal 

[bumper]

Planning a trip to Mull.

Get to Oban, get ferry to Craignure, tell world+dog to get stuffed for n days. Simples

Spot on!

You must have a little tipple at least once when you're there. My hip flask is permanently in the camping gear, purely for medicinal purposes you understand. Just to keep the chill off at night

[interzen]

Planning a trip to Mull.

Get to Oban, get ferry to Craignure, tell world+dog to get stuffed for n days. Simples

Spot on!

You must have a little tipple at least once when you're there. My hip flask is permanently in the camping gear, purely for medicinal purposes you understand. Just to keep the chill off at night

Sadly, my dysfunctional pancreas means that alcohol is pretty much a no-no, which is doubly painful if I go to Islay because I was a big fan of Islay malts; the smokier/peatier the better.

I can recommend the distillery tour at Tobermory if you haven't done it - last time I did it they were doing free samples during the tour

[bumper]

Love the distillery tours. Well, love the tasting at the end

[tiermat]

Meanwhile, back at the bat-cave, I am on hold to Trez, trying to sort out my gift vouchers that I got for Xmas.

This might tale a while...

[matthew]

Love the distillery tours. Well, love the tasting at the end

The tasting is an important part but as a Biochemical Engineer, the fermentation process is highly interesting.

When at Bladnoch a couple of years ago I ended up with a one to one tour due the lack of demand. This resulted in being able to ask questions about the stills that the guide couldn't answer.

When I was in Tobermory last year the cruise ship was in port so the tours were heaving. Talasker later in the same trip was less busy but still too busy for awkward questions.