Candy Dulfer

Lets hope that her birthday is good news for Great Britain ,,, and we are still together and look forward into a future of togetherness and peace …

How to get to 6 ? Solutions …

Here is one set of solving equations: (0! + 0! + 0!)! = 6 (1 + 1 + 1)! = 6 2 + 2 + 2 = 6 √(3 * 3) + 3 = 6 √4 + √4 + √4 = 6 (5 / 5) + 5 = 6 6 – 6 + 6 = 6 7 – (7 / 7) = 6 8 – √(√(8 + 8)) = 6 √(√(9 * 9)) + √9 = 6 I must admit thta I had to look up the factorial definition again … but it is true 0! = 1 . What is zero factorial? Also see the youTube clip where I got it from. Quite...

Patterns in the Fibonacci Numbers

Here are some patterns people have already noticed in the final digits of the Fibonacci numbers: Look at the final digit in each Fibonacci number – the units digit: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, … Is there a pattern in the final digits? 0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, … Yes! It takes a while before it is noticeable. In fact, the series is just 60 numbers long and then it repeats the same sequence again and again all the way through the Fibonacci series – for ever. We say the series of final digits repeats with a cycle length of 60. Suppose we look at the final two digits in the Fibonacci numbers. Do they have a pattern? 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, … Yes, there is a pattern here too. After Fib(300) the last two digits repeat the same sequence again and again. The cycle length is 300 this time. So what about the last three digits? and the last four digits? and so on?? For the last three digits, the cycle length is 1,500 for the last four digits,the cycle length is 15,000 and for the last five digits the cycle length is 150,000 and so on… >> Go to Source...

Why 12 notes to the Octave?

Here is the beginning of an exhausting explanation … The Greeks realized that sounds which have frequencies in rational proportion are perceived as harmonius. For example, a doubling of frequency gives an octave. A tripling of frequency gives a perfect fifth one octave higher. They didn’t know this in terms of frequencies, but in terms of lengths of vibrating strings. Pythagoras, who experimented with a monochord, noticed that subdividing a vibrating string into rational proportions produces consonant sounds. This translates into frequencies when you know that the fundamental frequency of the string is inversely proportional to its length, and that its other frequencies are just whole number multiples of the fundamental. (actually, the notion of consonance is more complicated than rationality- see, for example, this fascinating article ). First, we should examine what ratios are “meant” to exist in the western scale. The prominence of the major triad in western music reflects the Greek discoveries mentioned above. Starting with the note C as a fundamental, we get the major triad from the 3rd and 5th overtones, dropping down one and two octaves respectively, obtaining ratios of 3/2 (G:C) and 5/4 (E:C) respectively. Two other prominent features in western music include the V I cadence, and the I,IV,V triads. Both reflect the importance of the 3/2 ratio, with the IV further taking into account the reciprocal of 3/2, namely 2/3 aka 4/3. Musically, the reciprocal ratio corresponds to going down rather than up. While 3/2 corresponds to going up a fifth, 2/3 corresponds to going down a fifth, and 4/3 corresponds to going down a fifth and up an octave....

How to get to 6 ?

Just came across this little youTube clip . Basically you should use only mathematical operators / functions to fulfill all equations below: 0 0 0 = 6 1 1 1 = 6 2 2 2 = 6 3 3 3 = 6 4 4 4 = 6 5 5 5 = 6 6 6 6 = 6 7 7 7 = 6 8 8 8 = 6 9 9 9 = 6 There are multiple ways to do this. Here is an example for an easy one … the 4: ( 4 – √4 ) + 4 = 6 So, please give it your best shots and if you want to focus on the toughies … just do 0, 1 and 8. Full solution will be shown on this blog on the 19th September...

Voronoi Tessellation

In mathematics, a Voronoi diagram is a way of dividing space into a number of regions. A set of points (called seeds, sites, or generators) is specified beforehand and for each seed there will be a corresponding region consisting of all points closer to that seed than to any other. The regions are called Voronoi cells. It is dual to the Delaunay triangulation. It is named after Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi diagrams can be found in a large number of fields in science and technology, even in art, and they have found numerous practical and theoretical applications. >> Goto Source Follow the link below to see an animated Voronoi Tessellation … be the wandering point … Voronoi Tessellation The Voronoi tessellation shows the closest point on the plane for a given set of points. This example updates the Voronoi diagram in response to mouse interaction! Colors by Cynthia Brewer; algorithm by Steven Fortune; implementation based on work by Nicolas Garcia Belmonte; interaction inspired by Raymond Hill. Also have a look on the base javascript library …...

John Venn and the Diagrams

Venn diagrams were introduced in 1880 by John Venn (1834–1923) in a paper entitled On the Diagrammatic and Mechanical Representation of Propositions and Reasonings in the “Philosophical Magazine and Journal of Science”, about the different ways to represent propositions by diagrams.[1] The use of these types of diagrams in formal logic, according to Ruskey and M. Weston, is “not an easy history to trace, but it is certain that the diagrams that are popularly associated with Venn, in fact, originated much earlier. They are rightly associated with Venn, however, because he comprehensively surveyed and formalized their usage, and was the first to generalize them”.[2] Venn himself did not use the term “Venn diagram” and referred to his invention as “Eulerian Circles.”[1] For example, in the opening sentence of his 1880 article Venn writes, “Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called ‘Eulerian circles,’ has met with any general acceptance…”[3] The first to use the term “Venn diagram” was Clarence Irving Lewis in 1918, in his book “A Survey of Symbolic Logic”.[2] Venn diagrams are very similar to Euler diagrams, which were invented by Leonhard Euler (1708–1783) in the 18th century.[note 1] M. E. Baron has noted that Leibniz (1646–1716) in the 17th century produced similar diagrams before Euler, but much of it was unpublished. She also observes even earlier Euler-like diagrams by...

1 + 2 + 3 + 4 + 5 + … = -1/12

Is the world going nuts ? What happened to mathematics ? The magical world of infinite series … Well, here is a clue: Think of 1 – 1 + 1 – 1 + 1 + … = 1/2 And of 1 – 2 + 3 – 4 + 5 + … = 1/4 But don’t take my word for it. There is a nice little clip … >> Go to Source...

How radio telescopes show us unseen galaxies

Our universe is strange, wonderful and vast, says astronomer Natasha Hurley-Walker. A spaceship can’t carry you into its depths (yet) — but a radio telescope can. In this mesmerizing talk, Hurley-Walker shows how she probes the mysteries of the universe using special technology that reveals light spectrums we can’t see. more...

Barber paradox

Suppose there is a town with just one barber, who is male. In this town, every man keeps himself clean-shaven, and he does so by doing exactly one of two things: shaving himself; or going to the barber. Another way to state this is that “The barber is a man in town who shaves all those, and only those, men in town who do not shave themselves.” From this, asking the question “Who shaves the barber?” results in a paradox because according to the statement above, he can either shave himself, or go to the barber (which happens to be himself). However, neither of these possibilities is valid: they both result in the barber shaving himself, but he cannot do this because he only shaves those men “who do not shave themselves”. >> Go to Source...

Tour de France – Le Tour

Or better for the first time The Le Tour – can the Sky Team pull it again ? They should ! Follow the most torturous sporting event which exists from the 7th of July >> Le Tour Web...

The DIY orchestra of the future

Absolutely fantastic … music always goes and very encouraging to see ideas to bring it back to the people … Ge Wang makes computer music, but it isn’t all about coded bleeps and blips. With the Stanford Laptop Orchestra, he creates new instruments out of unexpected materials—like an Ikea bowl—that allow musicians to play music that’s both beautiful and expressive. Both a musician and a computer scientist, Ge Wang turns ordinary MacBooks and iPhones into complex...

Kolumba

Extraordinary architectural building combining new and old and spirit and space … Definitely worth a visit when in cologne. Kolumba is the art museum of the Archdiocese of Cologne, originally founded in 1853. Since 2004, the museum has borne the name of its new location amidst the ruins of the late Gothic parish church of St Kolumba, thus providing a spiritual home to the collection. A triad of place, collection, and architecture, it allows the visitor to experience two millennia of western culture in a single building. Comprising art from late antiquity to the very present, the whole ensemble is imbued with a still reverberating sense of history – visibly intensified through its distinctive architecture. The modern building is a harmonious combination designed by Swiss architect Peter Zumthor (2007) to merge both the Gothic ruins of St Kolumba and Böhm’s chapel »Madonna in the Ruins« (1950) with the unique archaeological excavation site (1973-76). Kolumba has been aptly termed »a museum of contemplation in which there is an ongoing dialogue between past and present« (Sarah McFadden, Art in America). Kolumba is curated by Stefan Kraus, Ulrike Surmann, Marc Steinmann und Barbara von Flüe. >> Go to Source Here are a few pictures to give you an...

Two poems about what dogs think (probably)

What must our dogs be thinking when they look at us? Poet Billy Collins imagines the inner lives of two very different companions. It’s a charming short talk, perfect for taking a break and dreaming … This talk was presented at an official TED conference, and was featured by our editors on the home page. >> Watch...

277,232,917 − 1

Largest known prime number As of June 2018, the largest known prime number is 277,232,917 − 1, a number with 23,249,425 digits. It was found in 2016 by the Great Internet Mersenne Prime Search (GIMPS). Plot of the number of digits in largest known prime by year, since the electronic computer. Note that the vertical scale is logarithmic. The red line is the exponential curve of best fit: y = exp(0.187394 t – 360.527), where t is in years. Euclid proved that there is no largest prime number, and many mathematicians and hobbyists continue to search for large prime numbers. Many of the largest known primes are Mersenne primes. As of June 2018, the seven largest known primes are Mersenne primes.[2] The last 16 record primes were Mersenne primes.[2][3] The fast Fourier transform implementation of the Lucas–Lehmer primality test for Mersenne numbers is fast compared to other known primality tests for other kinds of numbers. Please read more in the original wiki page >> click here to open the wiki...

Scientists reveal drinking champagne could improve memory

… I knew it … something in me was saying the same … if I just could remember … och, another glass might help ! New research shows that drinking one to three glasses of champagne a week may counteract the memory loss associated with ageing, and could help delay the onset of degenerative brain disorders, such as dementia. Scientists at the University of Reading have shown that the phenolic compounds found in champagne can improve spatial memory, which is responsible for recording information about one’s environment, and storing the information for future navigation....

Gödel, Escher, Bach

A must read for all who want to know about infinity … almost good enough to provide a foundation … but then it is just a carpet floating mid air as long as you don’t open your eyes … Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter, described by his publishing company as “a metaphorical fugue on minds and machines in the spirit of Lewis Carroll”.[1] By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, GEB expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of “meaningless” elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of “meaning” itself. In response to confusion over the book’s theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms. In the book, he presents an analogy about how the individual neurons of the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.[2][3]… >> Go to Source...

Moving Geometry – Time

The Linear Cycle Clock’s unique time display offers a playful alternative to the common circular dial. Sometimes it even moves … time is a miracle … >> Go to...

Miles lives

Oh my oh … he is the man … you might say was , but no – is and always will be . Strange but I always listen to his music and think of Mozart. Well, could ramamble for ages here but better behave now. As usual below is a quick link to the inevitable wiki site . Just one hint, in case you are scared of jazz or believe it’s not for you – try Kind of Blue ! Miles Dewey Davis III (May 26, 1926 – September 28, 1991) was an American jazz musician, trumpeter, bandleader, and composer. Widely considered one of the most influential musicians of the 20th century,[3] Miles Davis was, together with his musical groups, at the forefront of several major developments in jazz music, including bebop, cool jazz, hard bop, modal jazz, and jazz fusion. >> Go to Source...

Math is the hidden secret to understanding the world

Always love it when there is someone connecting the great topics : art, music, mathematics … Here is a nicely done TED by Mr. Roger Antonsen … what a guy … Unlock the mysteries and inner workings of the world through one of the most imaginative art forms ever — mathematics — with Roger Antonsen, as he explains how a slight change in perspective can reveal patterns, numbers and formulas as the gateways to empathy and understanding. >> Watch it...

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