Eunoia
 
> Most recent Blog Comments Policy DSGVO Impressum Maths trivia Search this site RSS Feed Eunoia, who is a grumpy, overeducated, facetious, multilingual expat Scot, blatantly opinionated, old (1944vintage), amateur cryptologist, computer consultant, atheist, flying instructor, bulldoglover, Beetledriver, textbookwriter, longdistance biker, geocacher and blogger living in the foothills south of the northern German plains. Not too shy to reveal his true name or even whereabouts, he blogs his opinions, and humour and rants irregularly. Stubbornly he clings to his beliefs, e.g. that Faith does not give answers, it only prevents you doing any goddamn questioning. You are as atheist as he is. When you understand why you don't believe in all the other gods, you will know why he does not believe in yours :) Oh, and he also has a neat English Bulldog called 'Kosmo'.
Some of my bikes
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My Maths Pages

Sunday, July 22, 2018
GuesstimatesBack on Friday, July 6, I blogged about doing exact multiplication quickly by mental arithmetic. Cop Car commented that she mostly uses guesstimates. So I've been trying to think of when I use guesstimates too, to get a quick approximate answer.So let me show you today how to calculate square roots by guesstimating. I'll show you three examples. To get the square root of (say) 41, use the next lower perfect square, 36, which is six squared. So the answer will be six plus something. To get the something, take the excess 5 (=4136) and divide it by twice the six, getting 6 + 5/12 = 6.41666 which is only about 0.2% high. Now try 51, so 49 is the nearest lower perfect square. So the answer will be seven plus something. That something will be the excess 2 divided by twice the seven = 7 + 2/14 = 7.143, instead of 7.142. Now try 137. So that's 11+something. The something will be 16/22= 0.727 making 11.727 instead of 11.705 so 0.2% off. You see, the guesstimates are quite good :)
Wednesday, July 18, 2018
Helsinki Body LanguageWho needs body language? The facial expressions say it all :( And we can't trust either of them :( Comments (2)
Sunday, July 15, 2018
Bastille Day BloopersYesterday was Bastille Day, much celebrated by the patriotic French. As usual there was a big military parade, but this year the parade included a couple of magnificent bloopers ;)The parade included a display by the national motorcycle display team demonstrating their skills, e.g. by riding in interweaving figureeight patterns.
Except that this time two of them collided and fell off their bikes with the whole
The next blooper involved the Patrouille de France, who traditionally fly along the Champs d'Elysee over the Arc de Triomphe, trailing a Tricolore
(the French national flag) of red, white and blue smoke behind them. Except that this time the outside plane in the blue team had been loaded with red smoke instead of blue!
Sacre bleu! Again with the whole
This much to the amusement of other nations who believed the French military flag is allwhite anyway ;)
Thurday, July 12, 2018
Lost LettersOne of the benefits of the internet is that it provides access to old  like a thousand years old  documents which would otherwise be hidden away in libraries, monastries etc etc. I've been trying  with difficulty  to read some old (english) documents and it seems they use some letters which are no longer in our modern alphabet.Singing : Where have all the letters gone, long time passing? Old English used the Futhark alphabet , socalled because instead of a,b,c... it went f,u,t,h,a,r,k... But I can't really read that runic stuff anyway. But some of the Futhark letters survived into the middle ages, the first I encountered was Thorn, written in upper case as Þ and in lower case as þ. It was the predecessor of "th" used nowadays, you may still see it on british pub signs "þe olde pub". When the French took over (1066ff), they didn't have thorn and so replaced it with a "y", hence you also see "Ye Olde Pub" in Britain. But it is still pronounced The and not Ye ;) Next I found Eth, written Ð and ð respectively. It came from the Irish regional accent and also evolved into "th". The ampersand & is still with us. The name came from "and, per se, and" because it was the final letter of the alphabet and stood on its own. Another cropped up frequently, Eng , written as Ŋ and ŋ. It has been replaced by "ng", e.g. in an ending. Some letters were graphemes, merging two letters such as "ae" and called Ash. The merge of "oe" was called ethel and was the transcription of the futhark rune Odal. I don't know how to display Ond, That, Wynn ,Yogh , the long S or the Irish G but they crop up too. We've lost 12 letters it seems. Don't think all alphabets have the modern English 26 letters either. Welsh has 29 letters not all of them being L ;) Italian (like Latin) has 22, German has 30 (counting 3 umlauts and β) and Hawaiian just 13. Cyrillic, Greek and Latin alphabets actually share 11 letters. And if you thought 26+12=38 letters were hard, try Slovak with 46 or Cambodean which has 74 :) PS: In Trump's tweets the letter I seems to crop up a lot ;) Comments (4)
Monday, July 9, 2018
Biker NewsGood knews from Kinga, who is riding her motorcycle back from Australia to Poland. She got safely through Iran, despite her big bike and her gender (officially motorcycles over 250cc are illegal in Iran and women are not allowed to ride). So now she just has to cross Aserbaidschan and Armenia (short rides) before the long eastwest trip across Turkey to reach Europe. I enjoy following her blog 'cos I'm too old to do that ride myself.The 5 of our lads who set out for a tour round the Baltic gave up and just toured southern Norway instead due to a mishap and bad weather. One ran off the road in Poland, breaking 2 ribs and damaging his kidneys. The bike was a write off. So the other 4 returned him to Germany where his GF picked him up. Replanning took those 4 to Norway where one chickened out due to incessant rain (so I've bought him a "Norsk sutrer" Tshirt ;) ) The remaining three turned south after Trondheim to get to warmer and dryer weather and did a tour of the fjords. Now all 5 are safely home again :) I've had lumbago which prevents me from riding right now. Originally I wanted to go to the LWL museum in Münster which has an exhibition about brains and even has slices of Einstein's brain on display. Macabre but interesting. More about that when I can make the trip :) Some bad news too though : William Dunlop was killed in a practicesession crash at the Skerries 100 road races in Northern Ireland, the third member of the family to die roadracing :( Comments (2)
Friday, July 6, 2018
Go forth and multiply....... it said in the bible. But it didn't say how to multiply ;)So here I'll show you yet another method to do mental arithmetic multiplication, this one suitable for numbers "near" powers of ten. Single digit example, just to illustrate the method : 7 * 8 =56 which you learned by rote, so you know the answer already. Now this new method: How far is 7 from the next power of 10? 3. So subtract that 3 from the other term 8, giving 5. Write that down on the left. How far is 8 from the next power of 10? 2. Multiply that 2 by the previous difference, 3, getting 6. Write that down on the right. So you've now written the answer, 56 :) Now a double digit example. 96 * 89 =? How far is 96 from the next power of 10? 4. So subtract that 4 from the other term 89, giving 85. Write that down on the left. How far is 89 from the next power of 10? 11. Multiply that 11 by the previous difference, 4, getting 44. Write that down on the right. So you've now written the answer, 8544 :) Sometimes the second product will be above 100, so just add the one to the left half of the result. Example with a carrydigit : 88 * 87. How far is 88 from the next power of 10? 12. Subtract 12 from the 87, getting 75. Write that down on the left. How far is the 87 from the next power of 10? 13. Multiply that 13 by the previous difference, 12, getting 156. Write that down on the right. This has 3 digits not 2, so you add the 1 to the 75 on the left, getting 76. The total result is thus 7656 :) Let's try three digits. 977 * 963 = ? How far is 977 from the next power of 10? 23. So subtract that 23 from the other term 963, giving 940. Write that down on the left. How far is the 963 from the next power of 10? 37. Multiply that 37 by the previous difference, 23, getting 851. Write that down on the right. So you've now written the answer, 940851 :) And you did all of that in your head! OK, OK, mostly people use a calculator (even the one in their mobile phone) but it's always useful to have another arrow in your mental arithmetic quiver. Comments (4)
Tuesday, July 3, 2018
Factorial fun!Sunday afternoon and five of us (bikers) were sitting in a quiet beergarden in the woods near Lake Möhne when a nearby belltower started to ring its bells. One of the girls asked "How long is that going to go on?" to which I replied "Well there are 7 bells, so 2½ to 5 hours, depending on the interval in which each bellringer pulls his bell.""How do you know that?" she asked. "I don't, I just calculated it in my head" I explained in reply, "We hear 7 bells, so a full peal means 5040 individual bellpulls  that's factorial 7  which takes almost 3 hours to ring. An 8 bell extent takes about 19 hours and has only ever been rung errorfree once, afaik." "What's a factorial?" she asked. "The number of ways you can arrange N items in a line. So factorial 3 is 6, and the 6 permutations are ABC, ACB, BAC, BCA, CAB and CBA. Factorial N is the product of all whole numbers up to N, so for 3 it is 1*2*3=6 and for 4 it's 1*2*3*4 = 24, for 5 it's 1*2*3*4*5=120, for 6 it's 6!= 720 and 7!=5040." "I remember doing that in school," one lad replied, "but we were never told what you could use it for. And the maths teacher said factorial Zero was One, but never told us why, and I didn't understand why that is so. And you can't put a zero in that 1*2*3... sequence!" "There are 2 ways to put 2 items in a line, AB and BA. There is just one way to put one item on the line. And there is also just one way to put zero items on a line. So factorial zero is defined as one." I replied. "But what about the sequence 1*2*3*4*5...? No zero in it!" I was asked. "Let's just rearrange the definition there" I answered "Four factorial is five factorial divided by 5, 3 factorial is 4 factorial divided by 4, 2 factorial is 3 factorial divided by 3, 1 factorial is 2 factorial divided by 2, and 0 factorial is 1 factorial divided by 1, which is 1" I explained. Meanwhile the full peal of bells had stopped because one of the bellringers had made a mistake; sometimes known as dropping a clanger ;) Combinatorial bellringing was first described by Fabian Stedman (GB) in 1668 in a book Tintinnalogia cowritten with Richard Duckworth and later in Stedman's own 1677 book "Campanalogia". Mathematicians thus see him as the first Group Theorist :) FWIW, the exclamation mark notation N! for N factorial was not introduced until 1808 by the French mathematician Christian Kramp. Comments (1)

Recent Writings
Guesstimates Helsinki Body Language Bastille Day Bloopers Lost Letters Biker News Go forth and multiply Factorial fun! 150 years of typewriters Canstein Highland Games Hilarious Blackmail Scams Are these Skyhooks? Brit Blades Ban On the road again :) G7 Body language Use less plastic! NSU motorcycle museum DSGVO Blogroll additions Marion's new book Dambusters' Day Jewish Birthdays Facial Asymmetry Celle Old Town The 26 D hypersphere Pied Piper snapshots Gauss @ 241 Find the page :) Blogroll Ain Bulldog Blog All hat no cattle Badtux... Balloon Juice Cop Car Curmudgeonly... EarthBound Misfit Fail Blog Finding life hard? Greg Laden Mockpaperscissors Mostly Cajun Not Always Right Observing Hermann On her Bike Pergelator Rants from t'Rookery Starts with a Bang Yellowdog Grannie Archive 2018: Jan Feb Mar Apr May Jun Archive 2017: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Archive 2016: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Archive 2015: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Archive 2014: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec This blog is getting really unmanagable, so I've taken the first 12 years' archives offline. My blog, my random decision. Tough shit; YOLO. Link Disclaimer ENGLISH : I am not responsible for the contents or form of any external page to which this website links. I specifically do not adopt their content, nor do I make it mine. DEUTSCH : Für alle Seiten, die auf dieser Website verlinkt sind, möchte ich betonen, dass ich keinerlei Einfluss auf deren Gestaltung und Inhalte habe. Deshalb distanziere ich mich ausdrücklich von allen Inhalten aller gelinkten Seiten und mache mir ihren Inhalt nicht zu eigen. This Blog's Status is Blog Dewey Decimal Classification : 153 FWIW, 153 is a triangular number, meaning that you can arrange 153 items into an equilateral triangle (with 17 items on a side). It is also one of the six known truncated triangular numbers, because 1 and 15 are triangular numbers as well. It is a hexagonal number, meaning that you can distribute 153 points evenly at the corners and along the sides of a hexagon. It is the smallest 3narcissistic number. This means it’s the sum of the cubes of its digits. It is the sum of the first five positive factorials. Yup, this is a 153type blog. QED ;) Books I have written

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