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Familiar Words From 1974
I started reading {a history of} π again yesterday. I read this some 12 years ago but wanted to read it again as I am going through some algebra fundamentals helping my daughter with her math exams. Almost 50 years ago, in the preface to the third edition from 1974 author Petr Beckmann wrote the following words that have lost non of their relevance : “Meanwhile, a disturbing trend away from science and toward the irrational has set in. … The disoriented and gullible flock in droves to the various Maharajas of Mumbo Jumbo. … Technology has wounded affluent intellectuals…
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Hummingbird
Hummingbird is a 2013 movie with Jason Statham. In the US it was released with the alternative title Redemption. Statham plays Joey Jones an ex special forces soldier with a history. After his patrol is ambushed in Afghanistan and 5 of his comrades are killed he takes revenge by killing 5 random ‘suspects’. He deserts and hides from the army living on the streets of London. One night; on the run for drug criminals he ends up in an empty apartment by chance. He shaves and cleans himself up. Urged by a Catholic nun from the food shelter he used…
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Bombelli’s Methode om Vierkantswortels te Berekenen
De Italiaanse wiskundige Rafael Bombelli bedacht in de 16de eeuw een methode om vierkantswortels te berekenen met een recursieve methode. Als we √n willen berekenen zoeken we een getal a ± r waarvoor n = (a ± r)2 met a een geheel getal en 0 < r < 1. n ligt hierbij tussen de kwadraten van a (bvb. voor 3 is a ofwel 1 of 2 want 12 = 1 en 22 = 4). Lossen we n = (a ± r)2 op naar r dan krijgen we r = ∣n – a2∣/(2a ± r). Met deze formule kunnen we recursief…
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Wondrous Arithmetic : Division
Remember having to divide numbers by hand ? If you have a rational number you can move from fractional form (a/b) to decimal form and back. Going from fractional to decimal form is done by performing the long division method. Going the other way is done using a ‘trick’. Any rational number written in decimal form will either have a finite number of decimal places or an infinite number of decimal places with some repeating sequence. In case of a finite number of decimal places it is simply a matter of removing the decimal separator by multiplying by the correct…
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Volkomen Kwadraten en Irrationale Getallen
Een irrationaal getal is een reëel dat niet kan geschreven worden als a/b met a ∈ ℤ (een geheel getal) en b ∈ ℤ0 (een natuurlijk getal). Een getal is een volkomen kwadraat als het het kwadraat is van een geheel getal. Een paar voorbeelden zijn 1, 4, 16 etcetera. Een ‘interessante’ eigenschap van volkomen kwadraten is dat ze altijd eindigen op een even aantal nullen (geen nul is ook een even aantal). Je kan dit inzien door naar de kwadraten van 1 tot 10 te bekijken die allemaal niet op een nul eindigen behalve 102 dat eindigt op 2…
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Perfect Squares & Irrational Numbers
An irrational number is a real number that cannot written in the form a/b with a ∈ ℤ (a whole number) and b ∈ ℤ0 (a natural number or whole number excluding 0). A number is a perfect square if it is the square of a whole number. A few examples are 1, 4, 16 etcetera. One ‘interesting’ property of perfect squares is that they always end with an even number of zero’s (no zero is also an even number of zero’s). You can see this is true by looking at the squares of 1 to 10 which all end…
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Wondrous Arithmetic
Here at home we just had exams again and I helped my daughter preparing for her math exam. We started doing this during the 2020 lock down and we have continued since then. Surprisingly enough I still know most of the math I got in high school more than 30 years ago. This is in stark contrast with other subjects like chemistry which I have mostly forgotten. This time one of the exam topics was trigonometry and during preparation I solved a problem coming to an answer that was different from the one given at the back of the book.…
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Wonderbaarlijk rekenen
Het waren weer examens en ik heb mijn dochter wat geholpen bij de voorbereiding van haar wiskunde examen. We zijn daar mee begonnen tijdens de lockdown van 2020 en ze had er blijkbaar iets aan dus doen we zo voort tot ze het niet meer nodig vindt. Het was verrassend voor mij dat ik na 35 jaar die wiskunde zelf nog allemaal in mijn hoofd had zitten. Hier en daar moet ik wel eens iets opzoeken en de formules ken ik niet meer van buiten maar verder zit het er nog in. Dit in scherpe tegenstelling tot bijvoorbeeld wiskunde waar…
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Genius. The Life and Science of Richard Feynman, James Gleick (ISBN 978-0679747048, Vintage)
After having reread the collected Feynman anecdotes from Surely You’re Joking and What do you care ? in the Classic Feynman edition I wanted to reread this biography by James Gleick again. The main reason being that the anecdotes focus on stories that happened to Feynman leaving out most of the science. Originally I read the stories again because I wanted to give them to my daughter to read as an unorthodox introduction in physics. But they are really ‘just‘ stories from a curious character as the byline in the title suggests. They are often funny, surprising and exceptional but…
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Fist of Fury
The second movie starring Bruce Lee. This is a classical story in the martial arts movie genre with a Chinese hero fighting for the honour of the Chinese agains foreign oppression and aggression. A superior Chinese martial artist is murdered after being poisoned by the Japanese. All typical Bruce Lee movie elements appear again with the noises, blood tasting and bare chested fighting. Compared to ‘The Big Boss’ the story is better this time as it is a classical storyline with the good Chinese against the bad Japanese oppressors. Many actors from the big boss return including James Tien, Nora…
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