Happy PI day · Celebrate Mathematics on March 14th
Source: Pi Day · Celebrate Mathematics on March 14th
Pi is irrational
Had my slice of pie today. Embrace irrationality 🙂
Happy PI day · Celebrate Mathematics on March 14th
Source: Pi Day · Celebrate Mathematics on March 14th
Pi is irrational
Had my slice of pie today. Embrace irrationality 🙂
And here it is again. The celebration of that beautiful number, the mathematical uniqueness that occurs in our life repeatedly, whether you realize it or not. This is PI day: Mar 14 (3.14).
Since I’ve been doing this the past few years, I’m not going to repeat all the fun facts about PI. But I will nevertheless give you some more interesting facts and links I found recently.
Things that equal Pi. Btw, the 360 blog has some really interesting posts and you should definitely subscribe to it.
Oh and of course, the recent appreciation of the reverent number even by politicians. Check this out.
And if you want to buy some swag for your PI day party, I suggest getting these beautiful PI shaped ice maker.
Update: Just found out that old Al’ was born on PI day. How fitting ?! Thanks to Neatorama for the piece of trivia.
Hmm.. Another year. Another day. Time is flying I tell you …
This is another one of those pun with math comic strips. Something along the lines of my earlier post last month.
Check out this strip from gocomics. Fox Trot.
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
A nice unfolding of the following infinite series expansion:
This is a very simple result. Can’t see it ? Work it out.
Archimedes, the original physicist and mathematician, was apparently responsible for coming up with the fundamental ideas for calculus. Although it might be safe to say that neither Newton nor Leibnitz actually knew this, they have to forego the privelege to having stumbled onto the thought first.
Here are more details from TheLongNow blog.
Whatdya know ?! Its PI day again. I remember posting on this day, last year about the same event and now, here we are again ! And in case you didn’t know, today is also the birthday of ‘Dr. Einstein’ of the E=mc2 fame 😉
Here’s a tribute to this magic number, π:
Biblical References: I Kings 7:23 II Chronicles 4:2
In Kings, it states, “And he made a molten sea, ten cubits from one brim to the other: it was round all about, and a line of thirty cubits did compass it about.”
In 240 B.C, Archimedes of Syracuse, Sicily (287 – 212 BC) did the first theoretical calculation of . He used methods similar to the ones used by Euclid by inscribing a regular polygon inside a circle. He started with a hexagon and then polygons of 12, 24, 48, and finally 96 sides. He also used one of Euclid’s theorems to develop a numerical method for calculating the perimeter of the polygons. Archimedes obtained the approximation 223/71 < π < 22/7.
150 A.D. Ptolemy found π to be approximately 377/120 (or 3.1416)
480 A.D. In China, pi was found to be approximately equal to 355/113 or 3.1415929 …
1150 Bhaskara (a Hindu) gave 3927/1250 as an accurate value of π
1579 Viete used polygons having 393,216 sides to evaluate π correct to 9 places
1610 Van Ceulen used 2^62 sides to compute π to 35 decimal places
1949 ENIAC (first modern computer) spent 70 hours to compute π to 2,037 places
In September 2002, π was computed to 1,240,000,000,000 decimal places by Professor Yasumasa Kanada at the University of Tokyo. It took over 400 hours on a Hitachi Supercomputer.
Book:
The life of PI – Here PI is an Indian guy’s name who gets stranded in the sea for more than 250 days. Its a good read although it has nothing to do with the π we are dealing with here. Just thought that might be an interesting trivia !
Movie:
PI – The movie starts with the line “When I was a little kid, my mother told me not to stare into the sun, so when I was six I did…”. Now with a line like that, how could i not watch it ! I’d recommend this movie to anyone who’s a little perceptive and frankly, a bit obsessed on math or anything for that matter. I watched the movie and loved it but few of my friends hated me for recommending the movie. So, there you go. But seriously, if you get some time, and are a math fan, watch it !
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The king sits in his central room and the n prisoners are all locked in their sound proof cells. In the king’s central chamber is a table with a single chalice sitting atop it. Now, the king opens up a door to one of the prisoners’ rooms and lets him into the room, but always only one prisoner at a time! So he lets in just one of the prisoners, any one he chooses, and then asks him a question, “Since I first locked you and the other prisoners into your rooms, have all of you been in this room yet?” The prisoner only has two possible answers. “Yes,” or, “I’m not sure.” If any prisoner answers “yes” but is wrong, they all will be beheaded. If a prisoner answers “yes,” however, and is correct, all prisoners are granted full pardons and freed. After being asked that question and answering, the prisoner is then given an opportunity to turn the chalice upside down or right side up. If when he enters the room it is right side up, he can choose to leave it right side up or to turn it upside down, it’s his choice. The same thing goes for if it is upside down when he enters the room. He can either choose to turn it upright or to leave it upside down. After the prisoner manipulates the chalice (or not, by his choice), he is sent back to his own cell and securely locked in.
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The king will call the prisoners in any order he pleases, and he can call and recall each prisoner as many times as he wants, as many times in a row as he wants. The only rule the king has to obey is that eventually he has to call every prisoner in an arbitrary number of times. So maybe he will call the first prisoner in a million times before ever calling in the second prisoner twice, we just don’t know. But eventually we may be certain that each prisoner will be called in ten times, or twenty times, or any number you choose.
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Here’s one last monkey wrench to toss in the gears, though. The king is allowed to manipulate the cup himself, k times, out of the view of any of the prisoners. That means the king may turn an upright cup upside down or vice versa up to k times, as he chooses, without the prisoners knowing about it. This does not mean the king must manipulate the cup any number of times at all, only that he may.
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I am not drunk and babbling gibberish. This is news. One fundamental theory which aims to make the use of trigonometry easier and more accurate. Proposed by Dr Norman Wildberger, a professor at University of New South Wales, this theory replaces angles to which we are so much used to by now, with a concept called as ‘spread’.
Here’s an excerpt from an article about this theory.
Established by the ancient Greeks and Romans, trigonometry is used in surveying, navigation, engineering, construction and the sciences to calculate the relationships between the sides and vertices of triangles.
“Generations of students have struggled with classical trigonometry because the framework is wrong,” says Wildberger, whose book is titled Divine Proportions: Rational Trigonometry to Universal Geometry (Wild Egg books).
Dr Wildberger has replaced traditional ideas of angles and distance with new concepts called “spread” and “quadrance”.
These new concepts mean that trigonometric problems can be done with algebra,” says Wildberger, an associate professor of mathematics at UNSW.
He has also written a book called ‘The Divine Proportions : Rational Trigonometry to Universal Geometry‘ by N J Wildberger. There is a chapter available for preview.
On first look, the concepts are straightforward in a logical sense. But i do not see how it simplifies and eliminates the calculations that are presently being done with sines and cosines. Well that’s just me and i could be wrong ! Maybe this is a revolutionary theory that is going to change how we look at things in the future.
A very interesting, perspective invoking picture of a 4D cube. Well ironically, its name is still a Cube in 4D.
Here’s a 4-D visualization of the cube in a raytraced Povray version of the picture.
Check out this site for more interesting trivia, facts and pictures related to math !