Eunoia
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> 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 after the death of his old dog, Kosmo, he also has a new bulldog puppy, Clara, since September 2018 :)
Some of my bikes
My Crypto Pages
My Maths Pages 
Monday, January 18, 2021
Laws of Nature 2.0Old friend Derek (Canada) sent these revised laws of nature, so I'm blogging them during my down time. All credit to Derek pls.
Comments (1)
Friday, January 8, 2021
Thank you GeorgiaThank you Georgia, for choosing both Democrat senators. Now we can expect a bit more peace and quiet; Biden/Harris can push their agenda through without obstruction from Moscow Mitch :)Just 12 more days until you can lock Trump up, USA :) Way to go! Comments (3)
Sunday, January 3, 2021
Solving quadratic equations another wayMy shortterm memory is worsening, so I'm kicking off 2021 with an anecdote from my longago schooldays instead.Back in secondary school we had a good maths teacher, Jeb, but who insisted we do things HIS way. I didn't like that. And thereby hangs this tale. Once, he was teaching us how to solve quadratic equations (see the equation on the left, below). Quadratic equations have at most two roots (since this is the highest power of x in the equation). So we had to learn by rote how to calculate these roots; see the equation on the right below. Remember, this was back in the days before calculators; calculations were either done in your head or with pencil and paper. This usually took the class 5 or 10 minutes; but I knew a faster way, using the irrationality theorem :) Suppose he wrote as the problem to be solved 4x^{2}  32x + 60 =0. In order to use the irrationality theorem, we need a=1 not 4, so I divided his problem by 4 getting x^{2}  8x + 15 =0. Now the irrationality theorem tells us that the roots of the problem are either whole number factors of c (here 15), or are irrational. Irrational means the number cannot be written as a ratio; so something like root(2) instead. Since this is only a simple secondary school problem, I reasoned that Jeb wouldn't give us a problem with irrational roots. So the roots had to be 1,3,5 or 15 (all the factors of c). Plugging each of these in turn mentally into x^{2}  8x + 15 =0 gave me the roots as 3 and 5. All this mentally in less than a second. So I could blurt out "3 and 5" before Jeb had even finished chalking the "=0" onto the blackboard :) Job done before he'd finished or the rest of the class had even started :) Results : class thought I was some kind of mental giant for using the equation on the right so fast. But only an A from Jeb for the right answer but not using his method; most unfair I thought. Not to say irrational ;) Jeb wanted me to show my working, so I wrote a cubic equation on the board x^{3}  7x + 6 =0. By the same reasoning, the roots can only be 1, 2, and 3. And since these are the 3 roots, there can be no irrational roots. And Jeb's equation (on the right) doesn't work for cubic equations, so my method was more general I claimed. What an obnoxious little knowitall I Comments (1)
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Recent Writings
Laws of Nature 2.0 Thank you Georgia Quadratic equations Give generously ? Dead Stick Landing Salmon Pie Local call from ET ? My last Great Conjunction MurderWitness ? Alexa! Roast me! French is not always... Not always 5 & 5 digits No More Fucking :( Local Lockdown Library Extreme Hotels The Sound of Silence Guten Morgan! Unlucky for some :( Biden Harris anagrams Flying the Shuttle Carrier NOT about the US election End of Days? Where's the Mass? A different Halloween Blogroll Ain Bulldog Blog All hat no cattle Balloon Juice Billions of Versions... Cop Car Digby's Hullabaloo EarthBound Misfit Fail Blog Finding life hard? Greg Laden Hackwhackers Infidel753 Mockpaperscissors Mostly Cajun Observing Hermann Pergelator Scotties Toybox Silicon Graybeard Starts with a Bang Yellowdog Grannie Archive 2020: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Archive 2019: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Archive 2018: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 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 : F?r alle Seiten, die auf dieser Website verlinkt sind, m?chte ich betonen, dass ich keinerlei Einfluss auf deren Gestaltung und Inhalte habe. Deshalb distanziere ich mich ausdr?cklich 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've written

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