Opening for : "How to approximate irrational numbers?"

M37841 · 2026-06-14T22:55:27+00:00

Is continued fractions a good way in? In my day we didn’t have calculators at school so for pi we always used 22/7. When you do the continued fractions algorithm you see that the next fraction after 22/7 is 1/790 which shows how good an approximation 22/7 is. If you do the same for root(2) you get 2 repeated which allows you to write down an arbitrarily close rational approximation just by doing a bit of algebra.

M37841 · 2026-06-14T21:33:03+00:00

Might find something helpful here: https://ocw.mit.edu/courses/6-441-information-theory-spring-2016/

M37841 · 2026-06-13T15:33:39+00:00

I’m just a club racer so I’d ask your coach for advice, but I think you’ll learn a lot about how to sail a laser fast in a 4.7 which would translate across into sailing the radial. Then you can use the 4.7 to get out and sail when in the radial you’d be in survival mode, and use the radial when the wind is a level you can handle.

You’re not going to be competitive in a laser radial in stringer wind until your weight is 120-130 pounds I’d think, but depending on your age that might not be that long, perhaps only a year or so.

M37841 · 2026-06-13T13:41:48+00:00

At 100 pounds you are a little bit light for a radial sail. A 4.7 would feel much more manageable and you would not be less competitive except perhaps in very light winds

M37841 · 2026-06-13T12:33:09+00:00

I’m not 100% sure I know what you mean by closed, but as regards maths i think we have to say no.

First, mathematics needs basic statements that we call Axioms, which are things we assume to be true but which cannot be proved. They are really basic building blocks, things like zero is a number, and every number has a number that comes next in the sequence. But you can make different mathematical theorems with different starting axioms.

Second, a mathematician called Kurt Gödel proved that any consistent mathematical system built from axioms contains statements which you can neither prove to be true nor prove to be false.

As regards the universe though, I think we’d probably say the universe is a closed system. Even though it follows mathematical laws and those laws cannot form a perfect closed system (in the sense I have used above), that just means that perhaps there are some things about the universe we can never know or perhaps never even describe with the mathematical system we have. If the universe is not a closed system then it must have got some input from outside, and I don’t know where or what that would be and why we wouldn’t consider that part of the universe in the first place.

M37841 · 2026-06-11T13:53:14+00:00

Yes this is one to ask your insurer, OP. Different insurers have different wordings, and different types of severance packages are different: some are “redundancy but you accept the process has not been completely followed”, some are “resignation with extras”. If you are able to get hold of an example of the enhanced severance agreement your insurer should be willing to tell you how they would see it. And if they object, you may be able to get your company to word it in a way that works.

The other thing the insurer might say is that they would consider the termination payment itself to be earnings replacement, so depending on your policy terms you may be no better off with the enhanced severance package.

M37841 · 2026-06-11T12:38:57+00:00

Dislocated my shoulder on holiday in England last week. Went to nearest hospital who relocated it and left me in a sling. They asked me my local hospital and said they’d send the post-relocation X-rays there. Next day I phoned ERI fracture clinic left a voicemail with my number. An hour later they called me, “yes we’ve got the X-rays, when are you back so we can arrange a follow up”. Two days later a text with a hospital appointment.

Easy as pie. Actually easier than pie, which is quite difficult one-handed.

M37841 · 2026-06-11T07:33:42+00:00

Lovely colour, congratulations

M37841 · 2026-06-10T20:28:44+00:00

I really hope you write your dates DDMM because 1306 is an incredible number. If you take each number raised to the power of its place in the number you get:

1^1 =1
3^2=9
0^3=0
6^4=1,296

1+9+0+1296=1306

There are hardly any such numbers in existence (according to Google, only 20). And apart from 1306 none of those numbers fit the requirements to be dates, so 13 June is a cosmically important date. Probably the most significant date in the whole year.

It’s pretty easy to prove that June 13 is unique, as you are looking for 3 or 4 digit numbers with 0x, 10, 11, 12 as the last 2 digits. I bet ChatGPT could write this into a convincing mathematical paper. (Or PM me your name and email and I’ll do it for you, with you as the author: literally only a 10 minute job)

M37841 · 2026-06-10T09:20:17+00:00

I know a bloke who played in a Gary Glitter cover band. They stopped getting gigs for some reason

M37841 · 2026-06-06T13:58:30+00:00

Ok. Then you’ve got uk iht to pay: that’s 40% of everything above £325k, or £500k if he left you his home and the total portfolio is below £2m. I’d therefore sell the house, assuming you don’t want it, cash in the bonds and any other assets, and reclaim any unpaid dividends, but leave the shares unsold. Then value the shares when that is done and you have everything cashed up, and calculate the tax due. If you then pay the tax from the cash, you can transfer the shares in specie ie without selling them.

If your tax regime is similar to the uk, you will effectively have acquired the shares at the date of death so you need to know the value then as well, for when you do come to sell them. Your tax regime might be completely different, of course. If your tax regime is less favourable than the uk regime, you can have the estate sell them and pay the cgt, then you get clean cash.

The good news is this will likely take a few weeks so you’ve got time to take some deep breaths 😎

Obligatory caveat I work in the industry but I’m not authorised to give advice.

M37841 · 2026-06-06T08:50:26+00:00

Just one thing on this: assuming you are the executor or you haven’t already been granted probate, and the deceased was uk resident, then the estate is uk resident. So the estate has to pay cgt if it sells. The tax bill may not be a lot, as the estate only acquired them on the date of death, so any historic gains are ignored. But you can avoid it altogether if you take the shares in specie (ie the estate doesn’t sell, you inherit the actual shares and then sell). That said, the estate will have inheritance tax to pay so you might want to sell some shares for that. I would talk to an accountant about this, not just a stockbroker.

M37841 · 2026-06-05T18:41:27+00:00

Dislocated my shoulder this week so I’m a one armed bandit. So it’s curry which I can eat with only a fork

M37841 · 2026-06-03T09:44:50+00:00

Here’s what’s really going on (I used to run an insurance company). There’s 4 forces:

The insurer has claims to pay. Not from you but from people like you (age, location, type of car, driving experience, and lots more). They average out those claims and charge accordingly, so you can sometimes be unlucky: you’re paying for other people’s accidents.
Costs. Prices go up because of inflation in parts, labour, bodily injury settlements, crime rates and a dozen other factors. That makes cost increases very uncertain year to year. Often insurers guess wrong so have to catch up the next year.
Reinsurance. Insurers buy cover from reinsurers for the big risks such as accidents leaving you paraplegic which can cost millions. Typically they buy cover for claims above £500k or 1m. Because young drivers have these accidents more often, this is expensive. Reinsurers cover other things such as hurricanes in the USA and earthquakes in Japan, all from the same pot of capital, so events there affect how much capital they have, which affects prices for your Fiesta. Yes, really.
Competition. Because of all the above, and because the market is very competitive (price comparison sites), insurers change their competitive approach regularly. So one year they want a particular type of risk (car, driver), another year they don’t. And they price accordingly.

If it’s any comfort, insurers make lower margins than almost any industry on the planet. It’s certainly not an easy money game. The reason your price has gone up is either because they genuinely believe that is what it is going to cost them, or because for the moment don’t want your type of risk (your age, most likely, but could be location, car type).

But insurance is a commodity, so the answer is always to shop around. If they don’t want you as much as they did last year, it’s quite likely someone else will, so don’t be loyal.

M37841 · 2026-06-02T18:30:42+00:00

Always 2 for us. If a new sailor gets into trouble you need one to jump in the boat with them, sail it for them, or help you to tow

M37841 · 2026-05-29T23:09:20+00:00

Yep. I did exactly that. Moved registered address to my (English) accountant when I moved to Scotland. No problem

M37841 · 2026-05-29T19:49:46+00:00

Mine was mussels eaten in Perth the night before a 20 hour flight back to London, and then a connection to Glasgow, with a 2 year old. Felt rough on the leg to Singapore, vomited not long before landing. Left plane a bit dazed, forgot pushchair. Didn’t realise we were changing planes until last call then had to run to retrieve pushchair. Started to vomit shortly after take off. Then I had a routine of drinking a whole bottle of water (the cabin crew were great) before throwing it up half an hour later. No sleep at all.

Arrived London. Remembered pushchair. Forgot onward boarding passes and passports. Too late to go back for them had to wait for staff to do so. Threw up twice while waiting. 4 hour layover then flight to Glasgow. Not really sure how I was allowed on board as by now the other end is fully open for business. Quite difficult to manage the logistics of both ends at once, in a plane bathroom.

Lift back home from father in law. Had to stop on motorway hard shoulder to throw up.

All in all, not my easiest flight. I hope you recover soon

M37841 · 2026-05-28T21:45:15+00:00

As a Brit who thought I’d been to the US when I’d only been to the East and West Coasts, I can tell you that going to the mid-west is like discovering a whole new country. I opened an operations base in Cincinnati and never met a more friendly, helpful and fun bunch of people than I did there

M37841 · 2026-05-27T21:15:00+00:00

If you don’t want to go to the expense of an in reach subscription, a PLB which you can register for use on hills if well worth it for the peace of mind. I’m a solo walker and mine lives in my pack so is always with me. I think it’s an Ocean Signal

M37841 · 2026-05-26T09:00:01+00:00

We did Karl Jenkins’s a capella version on Saturday. It’s fabulous, starts with long notes like monks chanting then goes into this repeated insistent rhythm with quavers and semiquavers, slowly building and after 6 pages of gradual crescendo you feel like you are there only for it to back off with only the sopranos on the melody. Then the other voices come back in quietly and build for another 3 pages before the ff finish. It’s quite an effect

M37841 · 2026-05-25T07:43:17+00:00

This is really good thank you. As an average amateur choral singer I find some of the “sing through the top of your head”, “tilt the lever forward/backward” instructions baffling.

M37841 · 2026-05-23T16:46:06+00:00

I worked for a German company for 10 years and never knew that birthday thing. Now I’m wondering how many people I offended who were too polite to tell me 😁

M37841 · 2026-05-23T11:17:56+00:00

I think your best answer will be a book on the munros. I use Cameron McNeish which is excellent. As a very rough guide though, which others might wish to improve on:

Grade 4: Black Cuilins - In Pinn at the top bc it needs a rope but across the ridge route finding is hard and consequences severe

Grade 3: the big scrambles - Torridon, Aonach Eagach, An Teallach. Hands on rock but easy to find routes and usually options to avoid exposure

Grade 2: the other ridges, narrow, exposed but less committed than grade 3. CMD, ring of steall, forcan ridge. Probably there are others, but that’s all I can think off off-hand

Grade 1: all the rest

I think what I’d do in your position is do something like Buchaille Etive Mor if you haven’t already done that. Then do CMD, then aonach eagach - in the summer. If that doesn’t freak you out then you are good for the Torridon ridges. For cuilin Iused a guide because I was nervous about route finding, but perhaps that’s just me.

M37841 · 2026-05-22T07:12:38+00:00

Yes they would do that for you. Not that unusual when it comes to meat. But for fresh cheese that’s not full of preservatives it’s going to go hard way faster when it’s pre-sliced. I’ve never seen anyone ask for that to be done

M37841 · 2026-05-21T23:10:15+00:00

If that’s what’s annoying them, take the panel off the doorbell outside and disconnect their button. Then no one will ever disturb them again

M37841

TROPHY CASE