two wheels of different diameter attached to each other at the center, roll along a straight line. since they have different diameters, the smaller wheel must slip. (see other stackexchange answers) Why do I not see the slippage in these videos:   ?
The paradox:    We have a circle and there is another circle with smaller radius. They are co-centeric.  If circle make full turn without sliding, both smaller and bigger circle make full turn too. If we assume that the passed road is equal to the circumference of circles. We have got smaller circle's radius is equal to bigger one's.  Unsatisfying Solutions I found:    "Do not assume that smaller circle's circumference is equal to passed road since the surface that contacts to the ground is bigger one. " // Okey but it does not explain the paradox, it explains just what is the wrong assumption (even does not explain why it is a wrong assumption.) It is undeniable that every point on both smaller and bigger circle will contact exactly one and only one point on their path. Therefore we can think that this is a bijective maps and smaller circle is isomorphic to bigger one. (Okey but ....)   Question: What is the true answer? What is wrong with the definition of circumference of a circle and relationship with its taken path.
I am new to the telecom simulations system specially multisim, which I am having a project that I want to simulate.  My project in (Analog Communications) is consisting to have FM Transmitter (Modulator) that accepts a generated signal (Sin, Cos) and get me the modulated output as a Graph.  I've found this FM transmitter circuit (3 km range):   ![two muppets][1]  and I am building that circuit on Multisim, and I failed. Because I faced many problems, first of, the variable capacitor symbol is weird here in the multisim, and the regular capacitor doesn't have variable options. Secondly, when I Use signal generator as (Sin, Cos), the output gets weird after 5 second of the simulation.  I want to show the input signal (before modulation) and the output signal (transmitted or modulated).  I guess my output result where not the as expected, as the signal (Sin with phase 90&deg;) is giving weird result of few seconds of simulating.  Below are screenshots of the simulation results within time.          Any ideas how to edit or fix the above circuit to have this output is similar to what it should be? "Whether" Vs. "If" Could someone please help me with these sentences? I need to know  Which one doesn’t sound natural? Which one is formal and which one is not?   A - I don’t know whether this word fits in the sentence. B - I don’t know if this word fits in the sentence.   C - I don’t know whether or not this word fits in the sentence. D - I don’t know if or not this word fits in the sentence.   E - I don’t know whether this word fits in the sentence or not. F - I don’t know if this word fits in the sentence or not.  For me only D doesn't work and sounds not idiomatic. Meanwhile for me all of these sentences can be used in both written and spoken languages. Do you confirm me? Enumerate paragraphs and subparagraphs like sections but with letters I'm using pandoc and in my template.tex exists this code to make the paragraphs and subparagraphs to behave like sections.  % Redefines (sub)paragraphs to behave more like sections \ifx\paragraph\undefined\else \let\oldparagraph\paragraph \renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}} \fi \ifx\subparagraph\undefined\else \let\oldsubparagraph\subparagraph \renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}} \fi   This code generate number like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.1 paragraph  1.1.1.1.1.1 subparagraph   How to change this code to enumerate with letter like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.a paragraph  1.1.1.1.a.a subparagraph It would be easier to ask for a user's password only once during registration.  The problem: The user could make a mistake while typing the password once because of hiding letters.  The solution: The user could have a toggle button for showing or hiding the password.    Working example with . This approach could be used on the registration or login page.   Are there any benefits to asking a user's password twice during registration vs just not masking the password? Why would you ask twice?  P.S. :        Users make more errors when they can't see what they're typing while filling in a form. They therefore feel less confident. This double degradation of the user experience means that people are more likely to give up and never log in to your site at all, leading to lost business. (Or, in the case of intranets, increased support calls.)   The more uncertain users feel about typing passwords, the more likely they are to (a) employ overly simple passwords and/or (b) copy-paste passwords from a file on their computer. Both behaviors lead to a true loss of security.      Update: I created a . So you may use it if you want to.    Update 2: .  Update 3: Internet Explorer 10 added a toggle password visibility icon. It looks like this:    Update 4: Article about .  Update 5: Example with . mysqldump, preserve update_time and modify_time attributes as listed by show table status from Does mysqldump preserve the create_time and update_time attributes that are output by show table status from?  If not, is there an option that does this?   it looks like mysqldump preserves this data if you export to XML. EDIT: Well the data is included in the export. Whether it's read in at the other end I'm not sure.  Is there a way to do this with a normal .sql dump? script to count files in a directory In C++, sizeof('a') == sizeof(char) == 1. This makes intuitive sense, since 'a' is a character literal, and sizeof(char) == 1 as defined by the standard.  In C however, sizeof('a') == sizeof(int). That is, it appears that C character literals are actually integers. Does anyone know why? I can find plenty of mentions of this C quirk but no explanation for why it exists. What vintage movie had this blue floating holographic head talking to some kind of military installation? Notation: Why write the differential first? How can I prove that the Cartesian product of two countable sets is also countable? Extruding surface while keeping the shape here is the picture of what I would like to get(example nr. 2). I need the edge frame to be same in width and length. Also the extrusion is on surface (without depth) I tried extruding region, but it did not give me the result I wanted.   I know I could just adjust the scale and do it manually, but that would be eyeballing without achievign accuracy. I would like to know if it is possible to extrude or inset while keeping the shape (even edge space) Calculate expected values using logistic regression coefficients The outcome of the logistic model is binary (0;1) - intervention that occurs in hospital (3838 interventions in 51096 cases). I am modeling the effect of age groups (60 to 74; 75 to 89 and 90+) and sex (female) on the outcome. My reference age group is male aged 18-59.  My logistic regression coefficients look like this:  intercept  -4.313 female      0.5117 age 60-74   0.4081 age 75-89   1.1761 age 90+     1.5612.   Corresponding odds ratios:  female      1.668 years60_74  1.504 years75_90  3.242 years90     4.764   Now I am trying to obtain a probability of an outcome = 1 for each case. What is the right way to do this? Problem with Non English(Farsi, ...) subtitle Why didn't Umbridge succeed in Slytherin? The new information released about Umbridge on Pottermore on Halloween was interesting in that it demonstrated how insidiously Dolores Umbridge applied her ruthless ambition over the years. From making her half-blood family disappear from public view, to oozing her way through the Ministry and up the ladder of success, basically unfettered -- although no one liked her as a person, despite her saccharine demeanor -- this woman was over and again awarded significant positions of power where she could do tremendous damage to others.   Some might see these as Slytherin traits. Some. &lt; shifty eyes > So I was surprised to read that while Umbridge was a Slytherin student at Hogwarts, she was consistently overlooked for positions of power and prestige within Slytherin itself.   Why didn't Umbridge succeed in Slytherin?  RESOURCE: Pottermore on Dolores Umbridge:  , Difference between a gerund acting as subject and an infinitive acting as a subject? I am wondering whether there is any difference between a gerund acting as subject and an infinitive acting as a subject. How to access the Keyboard Layout Options in 13.10+ Show that $PF.PG=b^2$ in a hyperbola If the normal at P to the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ meets the transverse axis in G and the conjugate axis in G' and CF be the perpendicular to the normal from the center C then show that $$PF.PG=b^2\space and \space PF.PG'=a^2.$$ We know that the equation of the normal at parametric point $P\equiv(a\sec\theta,b\tan\theta)$ is given by  $$a\,x\cos\theta+b\,y\cot\theta=a^2+b^2$$   Equation of the transverse axis is $y=0$ and that of the conjugate axis is $x=0$.   Hence   $$G\equiv(\frac {a^2+b^2}{a}\sec\theta,0), \, G'\equiv(0,\frac {a^2+b^2}{b}\tan\theta)$$  C is the origin and CF is perpendicular to the normal. Hence   $$ CF\equiv b\,x\sec\theta-a\,y\tan\theta=0\implies y=\frac {b\,x\sec\theta}{a \tan\theta}$$   Substituting this in the equation of the normal we get   $$a\,x\cos\theta+b \,\cot\theta\,\frac {b\,x\sec\theta}{a\,\tan\theta}=a^2+b^2\ $$   implies  $$ (a^2 \cos\theta \sin^2\theta+ b^2\cos\theta)x=(a^2+b^2)\sin^2\theta$$  After finding the coordinates of F, the calculation becomes very complicated. So is there an easier way to approach the problem? I would love to see a pure geometric solution to this problem. What is a contrast matrix? What exactly is contrast matrix (a term, pertaining to an analysis with categorical predictors) and how exactly is contrast matrix specified? I.e. what are columns, what are rows, what are the constraints on that matrix and what does number in column j and row i mean? I tried to look into the docs and web but it seems that everyone uses it yet there's no defition anywhere. I could backward-engineer the available pre-defined contrasts, but I think the definition should be available without that.  &gt; contr.treatment(4)   2 3 4 1 0 0 0 2 1 0 0 3 0 1 0 4 0 0 1 &gt; contr.sum(4)   [,1] [,2] [,3] 1    1    0    0 2    0    1    0 3    0    0    1 4   -1   -1   -1 &gt; contr.helmert(4)   [,1] [,2] [,3] 1   -1   -1   -1 2    1   -1   -1 3    0    2   -1 4    0    0    3 &gt; contr.SAS(4)   1 2 3 1 1 0 0 2 0 1 0 3 0 0 1 4 0 0 0 Putting a matrix inside of caption gives \caption has an extra } From Manila to Canada via France and Italy I intend to apply for a tourist visa to Canada and a tourist Schengen visa. My itinerary will be from Manila to Paris, France to Rome, Italy then Canada where I plan to visit/stay for 2-3 months with an invitation letter from my daughter who is a permanent card holder. I understand I have to buy a return  ticket from Canada to Manila where I reside. Is this a feasible itinerary?  Will this affect my chance of getting a Schengen or even a visa to Canada as this is my first time to apply for a tourist visa to these countries although I have been to several countries in Asia like Japan, Korea, Hongkong, Macau, Singapore, Thailand, Malaysia, Indonesia, Vietnam, Cambodia to name a few. Will the consul in the France Embassy here in Manila look for a return flight from a member country to Manila?