Impersonational

It feels sometimes like waiting for the bus before there was real-time information about where the next one was, when eventually three would arrive together, so the first one is the standard warning which you may not need to read, and given the length of Coco’s musings he knows that at least one of you, dear readers, having chastised him off on several occasions for his wordiness, shall not read it. Many of you will be very well aware of the issue, and perhaps have no need to read any more than the next few words.

If you get a friend request from Coco (but unlikely if you are already friends 😉), or one of his other friends, followers or followed, or one impersonating one of these or impersonating him, then please check it out carefully first. Check it out even if it comes as what appears to be a legitimate friend suggestion from the moderator or owner of the source.

One of you not so long ago spotted a fake, impersonating public profile, from which Coco, amongst he supposes many others, had received a befriending request, and kindly advised of its existence. Thank you for doing so.

Coco has recently become aware that a number of such profiles has been set up. For the sake of privacy he shall not disclose here any names, it is not his place to do so, but advise that though you may find similar names or descriptions among his friends, the impersonations and impersonators are not there. Beware though for some impersonating profiles may have friends with other fake, impersonating profiles which help them to look legitimate.

It is perhaps worth checking from time to time for pages similar to your own – why would anyone set up a fake page of me you might ask, so does he? but people do. Coco thought little of the first one that he saw, at first, but there are many dangers here. Some public fora have tools to report pages which impersonate others. Whether they are effective, remains to be seen.

As for the other two omnibus, they have already left the stop should you have spent time reading this post whilst waiting…

Happy Christmas

Gnats and camels

It was an amusing tale in the published by the BBC Council’s clean-up warning for St George’s crosses but also the co-incidence with an article published by the LICC that prompted Coco. We do so easily see the gnat, but fail to notice that there is a camel in our beaker of notoriously middle-class or upwardly-mobile freshly ground and brewed, steamed, iced, skinny, but extra hot, caramel latté (Coco’s judgement on that drink: ).

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Circles

How often have you gone round in circles?

Resisting the temptation to look at the comments where there may be an answer to the puzzle which at first you thought was proving difficult only because you had not spotted the correct approach to the solution, you slowly begin to discern that in order to solve it it may be that you need one more piece of information. What do you do? Like every good student sitting an examination or test, you read the whole question again, carefully this time, looking for that one additional piece of information that will cause the solution to appear, rather like those pieces of art which you must examine with cross-eyes to see what is really there, out of the mass (mess?) of mathematical nonsense that already litters the page, but it is not there. You have found all of the information that is to be had.

You try again this time to establish what the missing piece might be which would allow a solution to be found. You discover that if you knew any one of three things there would be a solution. You look for all three things in the information provided, only to discover that it is still not there. At that point you open up the comments on the question to find several answers, but they are all different. How could that be? There is only one correct answer, but the respondents are quite sure about their own answers. You also see that there are others who have understood correctly that insufficient information has been given: some even point out that the assumptions made by those who have found an answer are both extraneous to the question, and unjustifiable on the information given.

In the light of this discovery it behoves those who are tempted to solve questions posted in this forum to ask whether there is sufficient information to find the answer before attempting to solve the riddle.

With that in mind, I thought I would pose one myself, not in its most generalised form, but then neither in the most simplified. We have three spheres in three dimensional space, whose sizes and locations we know. A fourth sphere lies between them and touches the surface of each of the other three. We want to know the size and location of the fourth sphere.

Without any more information we must be content to describe the locus and radii of all spheres that satisfy the touching condition.

The additional piece of information you need is that the centre of the fourth sphere lies on the same plane as the centres of the other three spheres.

Aside you will find a diagram, in which the z-axis has been rotated so that it is vertical to the plane that all four spheres hold in common.

E&OE If you do think you need more information, please raise your hand.

Ans. There are two solutions, one for an inner circle as above, the other for an outer circle. If the solution is progressed correctly both solutions should also fall out:
(2.593190781, 0.467232119, 2.480014276(=(-97465+3*4*√5*√19*√37*√47*√893)/19471)) ) (3.33644816961878, 2.48464503182240, 12.49131313089260(=(-97465-3*4*√5*√19*√37*√47*√893)/19471)))

Epic

Some say that mathematics is difficult, and the more proficient you become in it, rather like English, the more difficult it becomes to comprehend. When questions such as What is 1? are asked and you are told that One is -e, you begin the grasp with credulity the ineffable complexity that is mathematics. You may then be told that Euler’s formula precisely defines all real numbers x by { eix = cos(x) + i sin(x) }. A mathematician somewhere will complain that having placed the equality within braces Coco thus invalidated what he had just proposed. Ah well, such is the world of the mathematician.

Picture of legendary Greek king Odysseus listening to the sirens.

The word epic springs to mind when setting out on the voyage of discovery that is mathematics, but have you ever considered whether epic is the right word to use? Epic comes to us from the Greek. We speak of epic poetry. For the Greek that is a poem that tells a story. It may be a short story or it may be a long story such as that of Ulysses (Homer’s Odyssey).

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Turkeys for Christmas?

Whilst it is voting day in the UK, it is quite a different day in the former North American colonies. One of Coco’s friends pointed him to The False Prophet Rising: Part 2 – The Merging of Church and State https://i.ytimg.com/vi/BaoI5FPWO5o/hqdefault.jpg. It was not something that would normally grab his attention. Listening to the analysis of a Trump speech at the National Religious Broadcasters’ Convention – 2/22/24 reminded him very much of encouraging turkeys to vote for Christmas and not letting them know that they are on the menu. Having no influence as far as the choice of their new president is to be makes the detail of the various presentations in some ways superfluous which is a view contrary to that of the BBC (see US election 2024: Why the world is watching so closely https://ichef.bbci.co.uk/news/2048/cpsprodpb/CB97/production/_132291125_whitehouse_976getty.jpg.webp).

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Genus reassignment

Times were very hard. The countryside was being squeezed by the urban population, rows and rows of solar panels were being placed not only upon the most productive arable fields but now even upon the pastoral land where sheep may have safely grazed. The panels it was true provided much needed shade from the summer sum, but the diminution of the number of animals put pressure on the economy of the canine population, making life very difficult for the wolves who had families to feed.

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Forgotten things

It is a quirk of time zones that today means different things in different places, and the tomorrow of GMT, may be the today of a different zone, though unlikely at this late hour to be the yesterday of any less further west than Hawaii.

With that in mind then, and understanding that already ten hours of today have elapsed where today is today, please kindly take note that that today is the day when some would have us to believe that nothing happened, but many interesting and disturbing things did happen on this day, some being so recent as to only achieve the silver Jubilee of their decadary this year.

We need only think of George III of Hanover, who was born on this day in 1738 to understand its importance for the later potential unification of the Saxon peoples of northern Europe, but for a closer personal connection an unnamed, for fear of infringement of the GDPR, lady was also born on this day failing to see the coronation of our late Queen by perhaps a mere thirty five hours.

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