What is the meaning of negative factorial?

As far as I have learnt, a factorial of a natural number means that the number is kept on multiplying to its predecessor number till the last number becomes 1.

Eg. N! = N. (N - 1). (N - 2)......3.2.1

Now what if we have something like (-2)!

Some would say it's negative infinity because of the following -

(-2).(-3).(-4).(-5) ........... Negetive Infinity

Same result is shown by #AlgeoCalculator.

My question is, why so? Isn't this result invalid because it doesn't go by the definition? -2 is not a natural number, then how can you calculate it's value? Also, when it's behind 1 on the number line, how would you expect it to reach 1 ?

It doesn't make sense to me.. What do you guys suggest?

Thank You ﻿
François Lagarde's profile photoJeremy Taylor's profile photo
If you're talking about purely factorial, then -2! is a bad question, and doesn't have a solution. I don't know about using gamma. But Numberphile has a good discussion about factorial and a good intro to gamma: Zero Factorial - Numberphile. He gets the equation for gamma wrong, but it's still a good intro.﻿
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A way that we can take part in testing Buffon's approximation method for pi using Phd student Tommy Ogden's simulator.  I'd not come across Buffon's Needle before.
I bet you all knew how to do this, didn't you?﻿
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Jack Martinelli

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Do you prefer topology or fields to represent space?﻿
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John Cook

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Approximation due to Ramanujan, accurate to 18 decimal places.﻿
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Happy #PiDay! Wondering how it's calculated? Check out my Pi in Python series which gets up to 100 million digits!  It starts easy with Gregory's Series, moves through Archimedes and Machin and arrives at Chudnovsky where it calculates 100 million digits in 10 minutes.﻿
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All the regression theory developed by statisticians over the last 200 years (related to the general linear model) is useless. Regression can be performed as accurately without statistical models, including the computation of confidence intervals (for estimates, predicted values or regression parameters). The non-statistical approach is also more robust than theory described in all statistics textbooks and taught in all statistical courses. It does not require Map-Reduce when data is really big, nor any matrix inversion, maximum likelihood estimation, or mathematical optimization (Newton algorithm). It is indeed incredibly simple, robust, easy to interpret, and easy to code (no statistical libraries required).﻿
Kermit Rose's profile photoRene Heinzl's profile photo
Having a better regression calculation procedure does not make the standard theory useless!﻿
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Here you can watch the Engineering Mathametics related Videos online..........
‪#‎dragonflyeducation     ‪#‎Engineering ‪#‎education‬Videos﻿
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SoGoSurvey celebrates #WorldMathsDay. Around the world, students take a break from standard lessons and participate in competitive math-themed games.﻿
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manar sughayer

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Mental math!.  The difference between 100 and the numbers may be single digit figures for easy application!﻿
Serkan Sipahi's profile photoFouad Mellouli's profile photoClaudio Borghi's profile photoEnrico Caleffi's profile photo
Ohhh! Didn't realize you did the operators above AND below the line. Thanks, +manar sughayer.﻿
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Jimmy Wong

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Since it is PI day, I will post a question I have been meaning to ask for sometime. Lets say there is a number a = 0.101001000..
Now clearly this number is non-repeating and hence irrational. However, this number will never have any other digits apart from 0 and 1.

Can we say that any particular irrational number (or maybe a set of them) contain within themselves all the possible sequences of digits we can think of? Some people are tempted to say that since pi is non-repeating, it will in fact contain all sequences of digits possible, but I do not think so. It could be that it itself has a non-repeating pattern or logic but we do not know it as of now.

My question is, is there a way to prove or disprove this? Or is this an open question?﻿
Kumar Aatish's profile photoHusain Alshehhi's profile photo
I asked this question on reddit and got a good response. The number in question is called a disjunctive number. There is a stronger condition called a 'normal number'. The Champernowne sequence/number is an example of disjunctive. However, there are no known normal numbers that are not specially constructed to have such a property.﻿
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Raphael Polanco

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Physicist Ethan Siegel brings us amazing #Pi  facts in his blog "Starts with a Bang!"﻿
Dierck Ziegler's profile photoShakti Malik's profile photoDoris Schleibinger's profile photoDraško Kokić's profile photo
i believe otherwise. √2 + 0 i is an imaginary number that is also a real number. ﻿
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John Redden

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2012 Median Pay: $101,360 per year ﻿
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Ahmed Zainy

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Happy PI day !
John Doe's profile photoNoel Torres's profile photo
+John Doe 3141 May(5) 9th would be a perfectly accurate Pi day. And no, two points in USA are not "around the world", not even if you go from Hawaii to Virgin Islands.﻿
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Happy Pi Day!

The number pi or π (approximately 3.14159265) is well known as the ratio of the circumference of a circle to its diameter. Although π is an irrational number, meaning that it cannot be expressed exactly as a fraction, it is possible to express the number as an infinite series. 

One of the simplest such series is π = 4 – (4/3) + (4/5) – (4/7) + (4/9) – (4/11)... The standard techniques of calculus can be used to prove that this series converges to π. Unfortunately, the convergence is very slow, meaning that one needs to write down a large number of terms to approximate π with any degree of accuracy.

The Indian mathematician Srinivasa Ramanujan (1887-1920) found some approximations to π that are much better than the above series. The formula for the infinite series at the bottom of the picture is due to Ramanujan. It converges so quickly that each successive term in the series computes a further eight decimal places of π. To give you some idea of how accurate the formula is, the approximation given by just one term is 9801/(sqrt(8)x1103), which works out as about 3.14159273001. This is accurate to eight significant figures, and has the first six decimal places correct!

This is a very impressive approximation from a mathematician who worked before the era of computers. Perhaps not surprisingly, Ramanujan's contemporaries were curious about where he got his ideas. The answer is quite interesting: while dreaming, he received visions of scrolls of complex mathematical content from his family goddess, Mahalakshmi of Namakkal.

Although he died at the age of 32, Ramanujan left behind a large number of mathematical results, and some of the best modern methods for computing π are based on his work. Ramanujan did not write up proofs for many of his results, although most of them turned out to be both correct and original. However, he left behind four famous notebooks of rough ideas, one of which was lost until 1976. These notebooks have inspired many papers by later mathematicians attempting to prove Ramanujan's results.

Relevant links
The Wikipedia page on approximations to π:

The Wikipedia page on Srinivasa Ramanujan:

A popular post by +Malthus John from Halloween 2013, showing the first infinite series I mentioned, carved into a pumpkin:

A popular post by me from August 2013 about π, featuring the digital art of Cristian Ilies Vasile:

(Disclaimer: I am from the UK, where March 14th is 14.3, not 3.14. Call me irrational, but I don't think that pi day is a real thing.)

#mathematics #scienceeveryday﻿
Tikie Stamatopoulos's profile photoKokul Karunananthan's profile photoJay Akula's profile photoPrasanth Chinta's profile photo
22/7 = 3.14  :)﻿
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David K. Waltz

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Geoffrey Transom's profile photoElmira Yu. Kalimulina's profile photoJosé Leonardo Hernández Benavides's profile photoAnthony James's profile photo
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What are your thoughts on this?
Tom Kimber's profile photoAlina Z.'s profile photopsher grant's profile photoDaniel Razo's profile photo
Good idea.﻿
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Yes! Knowledge

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There's mathematics everywhere, in the nature as well.
One example and a rather beautiful one is *The Koch snowflake*.

"_On a continuous curve without tangents, constructible from elementary geometry_" (original French title: Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire) by the Swedish mathematician Helge von Koch.


Start with an equilateral triangle T=S(0).

Scale T by a factor of 1/3 and place 3 copies along each of the three sides of T as illustrated in the diagram below to form a new image S(1).

Next scale T by a factor of 1/9 = (1/3)2 and place 12=4×3 copies along the sides of T(1) as illustrated to form the image S(2).

For the next iteration, take 48=4×12 copies of T scaled by a factor of 1/27=(1/3)3 and place them around the sides of S(2) to form the image S(3). Continue this construction.

The Koch Snowflake is the limiting image of the construction.

The sequence of sets S(0), S(1), S(2), S(3), .... that are constructed this way form a Cauchy sequence in the Hausdorff metric, and the limit is the Koch snowflake

if you want to know more,

here's a much detailed explanation:

Great video on the topic by khanacademy﻿
Paulo Santos's profile photophilippe roux's profile photoEmma Herea's profile photoChaitanya Sindagi's profile photo
Very nice, but where is the Koch Snowflake found in nature? I don't think it matches real snowflakes...﻿
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