studiot

So what other sequence(s) start of like fibonacci but diverge from this pattern further down the line ? This is an exercise in thinking out of the box.

If it were fibonacci the next two numbers would be 8 and 13, swince 8 = 5 + 3 and 13 = 8 + 5

I have a different answer, though I see I miswrote the sequence. Abject Apologies, I can still change it. 9, 18

1, 1, 2, 3, 5... Why is this not a fibonacci sequence and what are therefore the next two terms ? Answers in a spoiler please.

I have been reading about the Erdos-Bacon distance and its central role in the success of the Google search algorithm. Fascinating.

As an author, presumably you want other people to read your stuff. Why do you expect them to do this if you can't be bothered to read the posting rules here ? I'm sure you have been told this before.

Whilst I agree with you that one purpose of education is to impart a level of knowledge and capability to avoid the pitfalls you mention education has several other purposes, especially in elementary school. Not least is to develop the ability to interact well with other people. Particulary worrying as children are becoming more and more isolated from others, behind screens, computers, phones etc. Equally, stuffing the early curriculum with Science doesn't shield anyone from a pushy and persuasive used car salesman. You also seem to have missed my main point that there are just too many subjects to to cover them all. Traditional Uk primary school concentrates on what are known as "The 3 Rrs" - "Reading, Riting and Rithmetic" supplemented with craftwork, painting and drawing, singing and perhaps dancing (once called music and movement), gardening, cooking, needlework, sport, telling the time, reading a timetable, a bit of history, geography, poetry, general knowledge. So no, I was not taught formal music. Furthermore your age range ( 10 - 14) runs at least 2 years into UK secondary education (high school). In that time basic STEM subjects would be introduced, along with foreign languages, woodwork, metalwork, religous educatio9n, music and formal instrument instruction. This is only a sample of the total list which again I stress makes it impossible to teach everything to everybody.

Your education curriculum must be severely limited. Tbere would just not be enough hours in the week to teach all available subjects to all pupils in aUK high scho I would never have been even an average art or music student no matter how long I remained at high school.

@joigus I think you are referring to what are often called the 'equations of constitution' (the Physics) and the 'equations of compatibility' (often geometric). A simple example from incompressible fluid mechanics would be Bernoulli's equation (an equation of motion ie one connecting time and space) is an equation of constitution. An equation of compatibility would be A1 V1 = A2 V2 where A is area and V is velocity. For pilot waves various possible equations of constiitution have already been listed, An equation of compatibility would need to modulate the amplitude of the pilot wave in such a way tha its amplitude is zero except in the vicinity of the particle. Does this help ? Sorry I'm having great trouble witth computers a the moment.

Was this a request for a simple guide to manifolds and spaces ? I have less than zero interest in Grok, but I can help with this. Again +1 for well put insight. This is a new variation on Sir Oliver Heaviside's famous remark to the Royal Society Gentleman, Should I refuse my dinner because I do not fully understand the process of digestion ?

This is a very pertinent question, which might be even better if you expanded on your second paragraph. +1 We have lots of different company models, in the UK, some for profit and some not for profit. Either way our glorious politicians have chosen to tax utility supplies to domestic consumers, so this is an additional cost which has nothing to do with either the ecological or engineering issues around winning the supply, generation or distribution.

Sadly my main pc has gone belly up some i am currently struggling with an old netbook. I have the prospect of a nice modern replacement complete with windows 11 pro. But w11 will not load my older copies of Office, which I need to use. I have discovered that there is a version still available that is not pay - as - you go but one time purchase namely office2024. But I see that some vendors are offrning this for £10 to £30 (allegedly legit) Whilst others are in the £120 to £200 range So I am asking Has anyone any experience of either or what is involved ?

Pretty useless dam if it only lasts 50 years with at 30% chance of flooding. Must have been designed by a university maths dept. 😀

Interesting point. I had a larger Kia for a while. A full charge is 64 kwh say 65 with charginging losses. 65 x 30 days = 1950 units if she had to charge it every day. Note you will not get a 15 kw rate from a standard UK socket it's 3kw from one socket or up to 8kw for a directly wired special outlet.

Thanks everyone for the replies. I do not know if US charging practice includes any form of fixed charges or 'standing charges'. In 2016 we removed the gas boiler and installed a heatpump so we are now all electric. Usage is spread out over the seasons as follows Summer 100 kwh per week for 14 weeks Autumn & Spring 200kwh per week for 30 weeks Winter 300kwh per week for 8 weeks Total 9800 annual kwh We had two cold/frosty weeks in December 2025 and the bill amounts to £300, including non negligible standing charges.

A few notes about the overcolourfull but untenable Heat Death. First and foremost it comes from the realms of classical thermodynamics, and preceded both Einstinian relativity and QM. Second it assumes the universe may be regarded as an isolated system. In this model there are two extremal 'drivers' to processes The Principle of Maximum Entropy The Principle of Minimum Energy. Both are system properties and since one represents a min and the other a max they often compete or work in opposite directions. But because they are independent it is also possible for one or the other to be inactive. There are oscillatory systems for which the entropy remains constant and thus are driven by the energy principle and are independent of entropy. Also since the models are of isolated systems energy remains constant. It should also be noted that energy is not a substance but a thernmodynamic accounting of energy that passes into or out of the system. Cosmologically this means that models that allow energy to leak or disappear or appear are not handled or included. QM complicates this by allowing energy to be temporarily 'borrowed' from somewhere else so long as the energy of the final system is lower than before. Cooper pairs and Higgs bosons provide good examples here.

As I said it it part of a larger scheme. Here is your question fully worked out (first 5 pages of Bonolo Non Euclidian Geometry)

(as KJW says) The deduction is:- If the sum of alpha and beta is not less than two right angles then l and m do not meet on the same side of the line as alpha and beta. There are three cases to consider, alpha plus beta < , > or = two right angles. Euclid does not start out assuming there are any lines in the plane that do not meet, that is his deduction shown in very short form by Stillwell. Heath's original translation goes into greater detail and even offers the original Greek.

The deduction is only valid if and only if the axiom is valid. Remember the axiom (they called it a proposition) is stated without proof.

The version of theaxiom you state is Euclid's own original. Even in his time there were several altbernative versions (eg Proclus, Arisole) aand much debate about he subject. What should be remembered is that Euclid built a coherent structure for Geometry and offered his version in line with the posiion in that buildup postulate 5 occurs. All the properties of parallel lines (apart from not meeting) are deduced by triangles after this raher as in your 'deducion' paragraph. What is your interest in his ? Many books have been written about this subject.

I had always been led to believe that US prices were well below UK prices but reading this BBC articlwe makes me wonder. BBC News'I had no electricity for six months': American families...Rising electricity costs have emerged as a key cost-of-living concern, pushing families further into debt. Over £1300 a month for electricity and rising ?

Part of this series of DVD lectures shows Dr Stewart in Western Australia picking up meteorites amongst some of the oldest rocks on earth at the surface ie billions of years old.

Z are the integers, not the natural numbers, N. "Find a natural number..."

Not quite sure about this since surely every number in N can be wriiten as the sum of 3 squares in R. For instance 14 = (3)2 + (√3.5)2 + (√1.5)2 and 28 = 14*2

No it is not a silly question but then it is also not a simple question (looks can be deceptive) . I did not answer before partly because of this and partly because a lot of things have been happening in my world just lately, not least including computer failure. The questions are actually quite deep and you would and a person would only need the answers if he was going to study the subject more widely. It would also require some preliminary work, but since you have come back and asked again perhaops you are up for that ? A good place to start would be to compare the normal distribution function with one half cycle of a sine function as they seem so similar at first glance. But they are actually quite different. The sine function is cyclic (important new term) The normal dist function is not cyclic. (exchemist is not quite right as the 'tails' stretch from negative infinity to positive infinity though it is almost never used in that way)