Stream

Join this community to post or comment

John Cook

Discussion  - 
 
If you shuffle a desk of cards well, there's a good chance that two cards that were next to each other before will remain next to each other.
If you randomize a long list of items, there's a good chance that two items that were neighbors before remain neighbors afterward.
8
1
Andy Payne's profile photoJohn Lato's profile photo
3 comments
 
This seems quite similar to the birthday paradox. In particular, while for any given consecutive cards the chance that they will remain together is quite low, in a full deck the chance that at least one pair will remain consecutive is reasonably high.

+Shubham Johri​ the article mentions it's assuming a "perfect shuffle", I.e. a uniform random distribution of permutations of the deck.
Add a comment...

Geppetto Null

Math Questions  - 
 
Hi all! This is a question about a concentration inequality and about how to effectively estimate the mean value of a function of random variables. If you wish, please take a look, thanks a lot!
http://math.stackexchange.com/questions/2104365/estimation-of-the-expected-value-of-a-function-of-a-random-variable
4
Add a comment...

Grazia Italiano

Challenges  - 
 
💛💚💙 This watch has been invented by me , using number 2 . And you ? Can you do it using another number ? 👄 
35
1
Grazia Italiano's profile photo
9 comments
 
+Amit Sukla , thanks . 💜 
Add a comment...

LEARN EASILY

Videos/Pictures  - 
 
This video explains how to solve some typical examples on limits & continuity - trigonometric limits.
39
7
Add a comment...

enlong chiou

Discussion  - 
 
Use right unit in experiment data can revealed surprise result just use simple math, for example : how many neutrino per square meter ? it take 6*10^14 neutrino(0.12 ev) which it's square root equal to proton's mass(93800 ev) have 8*pi/3 unit, neutrino 0.126 ev change it's unit into mass by divided by c^2 equal to pm^(2/3)(up quark)(1.4*10^-18 kg) which for neutron decay into proton by weak force from change down quark into up quark, vacuum energy ch relate to gravity by l = gm/c^2(black hole at Planck's length) to m*l = h/c = pm*pl devided by unit 4*pi/3 and pl = g(p)*(4*pi/3)*pm/c^2 (micro black hole of proton) , g(p) is ratio of strong to gravity force, by electric force between proton and electron relate to neutrino can deduced speed of light for EM force, all of this simply use right unit can have insight on united all force.
10
Valdis Klētnieks's profile photoKayan El's profile photo
3 comments
 
+Valdis Klētnieks My thoughts exactly =)
Add a comment...

Kevin Clift

Videos/Pictures  - 
 
 
Pound Coin

I remember when the odd-looking and odd-sided 20p and 50p coins were first introduced to the UK with decimalisation in 1971, and the questions that were raised at the time, about not being round and whether or not they would work in money-counting machines. They did – because Geometry!

Now someone, possibly a politician, has decided on a new coin with even more sides and an even number of them to boot. We will have to wait until March to see how well they will work in money-counting machines that rely on gravity and coin rolling since these new Pound Coins won't have a constant width.

So what's the problem? One feature of the new coin is that it's twelve-sided, rather than round. It's not the first non-round coin in circulation — 20p and 50p coins are seven-sided — but it'll be the first with a variable width. This means that it won't roll as well as other coins, a fact that some people fear will cause problems in cash handling equipment. The trouble is that twelve is even while seven is odd.

More here (Maths Plus article): https://goo.gl/nCiWMK

📖
The government acknowledges that a shaped coin may present a challenge to existing coin lock mechanisms configured to accept the current £1 coin only, and so will continue to engage with manufacturers in order to mitigate potential disruption. However, responses to the consultation indicate that the long lead-in time means that upgrading should be possible at a modest cost (and manufacturers may choose to offer this as a complementary or routine service). The consultation process also highlighted a number of alternative and innovative solutions currently in the marketplace for coin lock mechanisms, many of which have been driven by the retail and leisure sectors.

More here (Govt. response (pdf)): https://goo.gl/AhbPDM

🎬
Find out how vending machines identify and sort coins in this clip from The Science Channel's "Deconstructed."

Video (YT -3 mins.): https://goo.gl/0J8AAC

📖
The New Pound Coin: https://goo.gl/XSXhTk

🎬
The new 12-sided £1 coin. Arriving 28th March 2017. The pound won’t be round for much longer.

The New Pound Coin (YT ~30 secs.): https://goo.gl/5mluxL


Image: Royal Mint https://goo.gl/FP3w0H








11
Richard Hellier's profile photo
7 comments
 
+Mark Hirschmann I've always found it interesting that if anyone (me included!) is asked what is a Dodecagon, they always reply "a 12 sided figure" but the literal meaning is, of course, a 12 angled figure.
Add a comment...

Grazia Italiano

Challenges  - 
 
💛💚💙 How would you do it ? 👄
5
Add a comment...
15 comments

Orkhan Alizade

Math Questions  - 
 
Can anyone, please, describe me, what N^T(N transpose) means here? Look at only to the last fraction.

I understand the role of (l - p) and ( || l - p || ) there. But I do not understand what N transpose does there and what is its role there.

Thanks in advance!
12
3
Orkhan Alizade's profile photoGato's profile photo
13 comments
Gato
 
+Orkhan Alizade http://bit.ly/2k5yDmx

in your case:

a = n
b = l-p
Add a comment...

Zach Cox

Videos/Pictures  - 
 
Making Math Visible
5
Add a comment...

About this community

Welcome to the Mathematics Community! Please read the community guidelines before posting: http://goo.gl/SjFp4. Here are the most import things you need to know: *Please check the Dr. Math FAQ if you've got a question that might be common. You might be posting about something that we've already seen numerous times. http://mathforum.org/dr.math/faq/ *Don't link-litter.* If you've found an interesting article that you think the Mathematics community needs to see, please share it! But we want to know why you think it's share-worthy. *No unrelated ads or spam.* *Don’t cheat on homework, classwork, or other exercises.* This community is not well-suited for homework help (see homework policy below), but it has zero tolerance for cheaters. Cheaters will be banned. *Categorize correctly.* *Keep posts relevant to mathematics in some way.* Wondering why your post was removed? Read the complete community guidelines.

Torolf Sauermann

Videos/Pictures  - 
 
 
Lamp Design – Sauermann 2017
22
LevKozlodoev's profile photo
 
Yup, Torolf is back, continuing to give us those good raytraced fractals.
Add a comment...

Isaac Calder

Videos/Pictures  - 
 
a nice solid I came across yesterday [V= 56, F= 78, E= 132]
symmetry is Oh [octahedral complete, horizont.]
24
2
Hendrik Boom's profile photo
2 comments
 
Looks like there are some reflections that swap colours -- yellow with blue.
Add a comment...

Amadeo Artacho

Videos/Pictures  - 
 
Capítulo 22 de Jugando con números … ¡Se nos “caen” los exponentes!
#matemáticas #curiosidades 
 ·  Translate
Este capítulo número 22 de "Jugando con números" nos trae unas curiosas sumas donde al "caerse" los exponentes se sigue cumpliendo la igualdad.
10
2
Add a comment...

AMIT PRAKASH PANDEY

Math Questions  - 
 
Why dy/dx + sin(dy/dx)=0 can not be written as polynomial?
I want to know what happens when we try to expand this or try to find a solution of these kind of equations like e^dy/dx or cos(dy/dx) 
1
Valdis Klētnieks's profile photoAMIT PRAKASH PANDEY's profile photo
3 comments
 
+Shubham Johri
Thanks! This is what exactly I was looking for.
Add a comment...

Charles Ashbacher

Event Announcements and Discussion  - 
 
In Memorium, Solomon W. Golomb
Charles Ashbacher

It is with the deepest regret that I announce the passing of Solomon (Sol) W. Golomb. Few mathematicians have the intelligence and foresight to create a new area of mathematics and Sol was one of them. His book “Polyominoes,” first published in 1965, codified an entire field of recreational mathematics and Sol invented the term “polyomino” in 1953. While a few problems involving polyominoes had appeared earlier, he was the one that made it a discipline.
A polyomino is a plane geometric figure formed by putting one or more square figures of the same size together by the edges. Polyominoes of any number of squares can be created, although the smaller structures are the most easy to work with. The number of polyominoes that can be created using n squares grows rapidly. There are 12 that can be made with 5 squares, 63,600 with 12 squares and approximately 7 x 10^31 with 56 squares. Therefore, the number of problems is effectively infinite. Sol’s series of papers that appeared in “Recreational Mathematics Magazine” in 1961-1963 are classic papers that introduced and expanded the field.
The most famous polyominoes are the pentominoes, the twelve figures that can be made with five squares. This term was also invented by Sol and many pentomino problems appeared in “Journal of Recreational Mathematics” over the years it was published. I got my start in writing extensive programs to solve recreational mathematics problems by creating programs to solve problems involving constructions using the two and three-dimensional pentominoes.
One of the beauties of the polyominoes is that no higher mathematical ability is needed to work with them. Basic problems can be given to elementary children and they can be created for any level of difficulty and the polyominoes are inexpensive to produce. I once reviewed a kit of pentomino problems designed for elementary school children to aid them in developing spatial orientation skills.
Sol is now gone but he left a legacy of mathematics that can be used to educate and entertain. I encourage all people with an interest in math to acquire and read one of the editions of “Polyominoes.” It is an addictive area of mathematics that can be read and understood by everyone.


13
4
Charles Ashbacher's profile photo
2 comments
 
I am very well of Tetris, having spent hours playing the game. However, while the polyominoes of Tetris are the most famous among the general population, in the context of my message, which is recreational mathematics, it is the pentominoes that are the most famous.
Add a comment...

Tim Brzezinski

Freq Posts/Tricks  - 
15
2
Add a comment...

George Mpantes

Select a category (spam trap)-->  - 
 
το θεμελιώδες θεώρημα του απειροστικού λογισμού

https://www.academia.edu/30734013/
 ·  Translate
3
Add a comment...

Nihar Gargava

Discussion  - 
 
This animation describes a deck transformation of the covering space of the wedge of two circles.
You can read more about this animation on my blog here:

https://goo.gl/qTyeuL
19
4
Refurio Anachro's profile photoNihar Gargava's profile photo
5 comments
 
+Refurio Anachro Hey thanks! That animation does look better! Thanks a lot! I'll use it on my blog.
Add a comment...