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PDF Editor FAQ

Which Devil Fruit (One Piece) would you want to eat?

My all-time favourite is Sir Crocodile's Sand logia, but any of the 11 canon logias I would be glad to eat TBH.These are, counting Sand (and in order of appearance in the show)Smoke (Smoker) appeared Volume 12 Loguetown (east blue)Fire (Ace) appeared Volume 18 Nanohana (Alabasta)Sand (Crocodile) appeared Volume 20 Alubarna (Alabasta)Lightning (Enel) appeared Volume 27 upper yard (Skypiea)Ice (Aokiji) appeared Volume 33 long ring long land (water 7)Darkness (Blackbeard) appeared Volume 46 Banaro Island (unknown location but Thriller Bark saga chronologically)Light (Kizaru) appeared Volume 52 Mangrove 37 (Sabaody archipelago)Magma (Akainu) appeared Volume 56 Marineford (Navy HQ next to red line and Sabaody)Mud (Caribou) appeared Volume 61 in the underwater depths between Sabaody and Fishman island (chronologically fishman island saga)Gas (Caesar) appeared Volume 67 in the abandoned government lab (Punk Hazard)Snow (Monet) appeared Volume 68 in Punk HazardAs you can see, these are few and far between, especially considering the numbers of the other types of canon devil fruits (75 paramecias of which at least 2 awakened and 1 special, 32 zoans out of which at least 5 awakened, 4 mythical and 4 ancient)So to summarize I would gladly eat any of these logias OR quite a few paramecias too many to list (but not anywhere near all of them) (those with useful abilities for everyday life like sprouting extra arms from the floor or stretching like rubber or performing complex medical operations without equipment among many others) OR any of the zoans which allow flight which are actually quite a few (birds and other winged animals or otherwise capable of flight) OR any of the rare breed zoans (those which account for animals and creatures long since extinct or that didn't exist to begin with)

What are some things that mathematics students know, but others don't?

I was waiting that someone will ask it. Was sick of same question about computer guys, and programmers.Let me tell you some-[math] \pi \neq 22/7 [/math]0.999999.......=1The Largest known prime number till this date is [math] 2^{57885161}-1 [/math]. It has [math] 17,425,170 [/math] digits. It is a Mersenne prime'Balls' can be square too.Everything you can do with ruler and compass, you can do with compass alone. For more info read this- Geometric construction with the compass aloneThe most famous theorem of mathematics- Pythagorean theorem- whose NCERT proof troubles school kids most, has more than 500 proofs, may be more than 1000's. Eli Maor wrote a book in which he showed 367 proofs that were distinct enough to bother writing about separately. " (The Pythagorean Theorem)"Yes, 1>0 needs a proof.​​​[math] 0 [/math] can be equal to [math] 2 [/math], if you work in field of characterstic 2 i.e. [math] \mathbb{Z}_2 [/math].Jordan Curve Theorem- It is a very tough theorem to prove that every simple closed curve divides a region into two parts, "interior" and "exterior".​​​​A mathematician Kurt Godel has actually proved that God exist!!The Proof-Gödel's ontological proofA shape with finite volume must have finite surface area- FalseGabriel's Horn is an example.There are more rational numbers than there are integers- False[math] i^i [/math] is real number.​​​​The Fibonacci sequence is encoded in the number 1/89- ( 1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034 ...)Too much beauty in one pic..In a room of just 23 people there’s a 50% chance that two people have the same birthday.​[math] 1+1/2+1/4+1/8+ \ldots \ldots =2 [/math]Joke based on this- Infinitely many mathematicians walk into a bar. The first says, "I'll have a beer." The second says, "I'll have half a beer." The third says, "I'll have a quarter of a beer." The barman pulls out just two beers. The mathematicians are all like, "That's all you're giving us? How drunk do you expect us to get on that?" The bartender says, "Come on guys. Know your limits.[math] 1+1/2+1/3+1/4+ \ldots \ldots =\infty [/math]Joke base on this- An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third orders a third of a beer. The bartender bellows, "Get the hell out of here, are you trying to ruin me?"A pizza that has radius “z” and height “a” has volume Pi × z × z × a.If you shuffle a pack of cards properly, chances are that exact order has never been seen before in the whole history of the universe.Explanation- A deck of 52 cards can be ordered in [math] 52! = 52 \times 51 \times 50 \times...\times 2 \times 1 [/math] ways. But 52! is a very large number: larger than[math] 8 \times 10^{67} [/math].How big is this number? Well, someone shuffling a deck of cards once per second since the beginning of the universe (believed to be about 14 billion years ago) would not have shuffled the deck more than [math] 10^{18} [/math] times.Zero is even number.Three Interesting Theorems-The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color.Brouwer’s Fixed Point Theorem (implication) says that if you take two sheets of paper, one lying directly above the other. If you crumple the top sheet (do not rip or tear the sheet), and place it on top of the other sheet, then there must be at least one point on the top sheet that is directly above the corresponding point on the bottom sheet! Do you believe that?Hairy Ball Theorem (Real life implication)- It states that given a ball with hairs all over it, it is impossible to comb the hairs continuously and have all the hairs lay flat. Some hair must be sticking straight up!​​​​It took Russell and Whitehead several hundred pages to prove that 1+1=2 in Principia Mathematica.Divisibility by 7-Remove the last digit, double it, subtract it from the truncated original number and if the result is a multiple of seven, then so is the original number, keep repeating till number is small enough.Random walk theory- A result by Polya states that in one or two dimension, a random walker returns to the origin infinitely many times but only a finite number of times in dimension 3 (or greater).Thus they say- "A drunk ant or a drunk man will always reach home but a drunk bird might not!Mathematician exclusive jokes-"The B in Benoît B. Mandelbrot stand for Benoît B. Mandelbrot."(If you know a little about Fractals)My Favourite- "A comathematician is a device for turning cotheorems into ffee." (Hint look up Paul Erdos quotes)."I went to visit him while he was lying ill at the hospital. I had come in taxi cab number 14 and remarked that it was a rather dull number. "No" he replied, "it is a very interesting number. It's the smallest number expressible as the product of 7 and 2 in two different ways."-Hint- Ramanujan's most famous story.Prof: "Give an example of a vector space."Student: "V"Why did the mathematician name his dog "Cauchy"? Because he left a residue at every pole. :PThe primary reason Bourbaki stopped writing books was the realization that Lang was one single person."Let epsilon<0."[math] \int 1/cabin \ d(cabin)= Houseboat [/math] {Don't forget the constant C (sea)}[EDIT]36. Wine/water mixing problem-In the wine/water mixing problem, one starts with two barrels, one holding wine and the other an equal volume of water. A cup of wine is taken from the wine barrel and added to the water. A cup of the wine/water mixture is then returned to the wine barrel, so that the volumes in the barrels are again equal. The question is then posed—which of the two mixtures is purer?Any Guesses?Answer- Both mixtures will be of equal purity.Yes it is a math (logic) problem. Here is the solution-37. Frobenius Coin Problem- You must have done a puzzle like " the largest amount that cannot be obtained using only coins of 3 and 5 units", Right? Answer here is 7 units. Answer to this type of problems is called Frobenius number.For the case of two denominations , say, a units and b units where a and b has no common factors other than one, there is a formula to get the answer i.e. Frobenius number, which is N= ab-a-b.But there is no formula for case with three or more denominations, but algorithms exist.

What are some mind-blowing facts about mathematics?

Isaac Newton's Principia Mathematica contained a simple calculation error that went unnoticed for 300 years.Newton invented calculus in about the same amount of time the average student learns it.2200 years ago, Eratosthenes estimated the Earth's circumference using math, without ever leaving Egypt. He was remarkably accurate. Christopher Columbus later studied him.The largest prime number ever found is more than 22 million digits long.The Millennium Prize is a US$1 million award given to whoever can solve any 1 of 7 math problems, but to date only 1 of the problems has been solved.2013 was the first year since 1432 that's a rearrangement of four consecutive numbers.The highest accuracy calculations at NASA use just 15 decimals of Pi.In many Israeli schools, algebra is taught without the use of the symbol "+" as it looks like a Christian cross. They use an inverted "T" instead.Taking Pi to 39 digits allows you to measure the circumference of the observable universe to within the width of a single hydrogen atom.The word ‘hundred' derives from ‘hundra' in Old Norse, which originally meant 120.Zero is the only number which can not be represented by Roman numerals.What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillionPlus (+) and Minus (-) sign symbols were used as early as 1489 A.D2 and 5 are the only primes that end in 2 or 5An icosagon is a shape with 20 sidesAmong all shapes with the same perimeter a circle has the largest area.Among all shapes with the same area circle has the shortest perimeter40 when written "forty" is the only number with letters in alphabetical order, while "one" is the only one with letters in reverse orderFOUR is the only number in the English language that is spelt with the same number of letters as the number itselfFrom 0 to 1,000, the letter "A" only appears in 1,000 ("one thousand")12,345,678,987,654,321 is the product of 111,111,111 x 111,111,111. Notice the sequence of the numbers 1 to 9 and back to 1.Have you ever noticed that the opposite sides a die always add up to seven (7)Trigonometry is the study of the relationship between the angles of triangles and their sidesAbacus is considered the origin of the calculatorHere is an interesting trick to check divisibility of any number by number 3.A number is divisible by three if the sum of its digits is divisible by three (3)Magic of number nine (9). Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9).If you add up the numbers 1-100 consecutively (1+2+3+4+5...) the total is 5050A jiffy is an actual unit of time for 1/100th of a secondHave you heard about a Palindrome Number? It is a number that reads the same backwards and forward, e.g. 12421Have you heard about Fibonacci? It is the sequence of numbers wherein a number is the result of adding the two numbers before it! Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so onAncient Babylonians did math in base 60 instead of base 10. That's why we have 60 seconds in a minute and 360 degrees in a circle.2,520 is the smallest number that can be exactly divided by all the numbers from 1 to 10.When number 1 is divided by 998001. The answer would give you a complete sequence from 000 to 999 in order.There are 177,147 ways to tie a tie, according to mathematicians.In 1900, all the world's mathematical knowledge could be written in about 80 books; today it would fill more than 100,000 books.Pizza has a radius of “z” and height “a”, and therefore its volume is Pi x z x z x a, which makes up Pizza.Multiplying 21978 by 4 reverses the order of the numbers: 87912.Π, e, φ, √2 are popular irrational numbers.Seven is most commonly used numeric in human culture. We have Seven Wonders, Seven Rainbow colors, Seven seas, Seven Dwarfs and Seven days of the week. Even James Bond is 007.Any two opposite sides of a dice, when added make 7.Number 7 is the most popular number of all. It is because of many reasons like this is arithmetically unique. It is the only number you can’t really multiply or divide and still keep it in that group.Zero is the only number with most number of the names. Zero is also called naught, nil, zilch, naught and zip.‘Google’ was derived from a misspelt word ‘googol’. Googol means 1 followed by 100 zeroes.Advanced mathematics need abstract thinking which computers cannot handle.

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