Reflection on a circle
Minimize the sum of distances between two point and a circle
Best way to specify whitespace in a String.Split operation How do I capture the moon and its surrounding context? I wanted to photograph the full moon against a beautiful deep blue sky. I ended up with blown-out highlights of the moon:    So I switched to spot metering and captured the moon, losing the blue sky in the process:    I want a single photo that shows both the moon and the surrounding context (in this case, the blue sky). Doing an exposure fusion in Photomatix Essentials did not help:    Nor did HDR fusion (again in Photomatix):    Notice that the detail in the moon was lost in both cases, and the sky was also messed up in both cases: exposure fusion lost the beautiful blue color, while HDR created more texture than was actually present in the sky. I toggled Photomatix's option to remove ghosts, but that didn't help, either.  How do I photograph the moon together with its surrounding context (in this case, the blue sky, but in other cases, a tree, buildings, etc) without blowing highlights or shadows? I'm using a Sony NEX-5R, with the longest focal length lens I have, and with manual focus when needed.  Thinking I should fuse the photos manually, I tried opening the images as layers in Acorn, with the darker photo on top and with opacity set to 50%, and tried all 15 - 20 blending modes (normal, dodge, lighter, darker, multiply and so on), but none of them seemed to work. I'm afraid I don't know enough to use layers effectively. What blending mode and opacity and order of layers should I use for this task?  I don't have Photoshop, but do have Lightroom 5, Acorn and Nik Collection.  (In case you are about to recommend software, please note my requirements: I use a Mac, I would be willing to pay $20-30, and I don't want to use command-line software.) Why is the derivative of a circle's area its perimeter (and similarly for spheres)? When differentiated with respect to $r$, the derivative of $\pi r^2$ is $2 \pi r$, which is the circumference of a circle.  Similarly, when the formula for a sphere's volume $\frac{4}{3} \pi r^3$ is differentiated with respect to $r$, we get $4 \pi r^2$.  Is this just a coincidence, or is there some deep explanation for why we should expect this? I have Opportunity-lookup field on Opportunity (self),  Scenario:   Opportunity A if select Opportunity B using lookup then Opportunity B's same lookup field automatically populate with Opportunity A.   I tried to achieve this using trigger - before insert/update but its failing as:  System.DmlException: Update failed. First exception on row 0 with id 006G000000DHaBlIAL; first error: SELF_REFERENCE_FROM_TRIGGER, Object (id = 006G000000DHaBl) is currently in trigger Oppy_before_INSUPD, therefore it cannot recursively update itself: [] How to edit Parameters for an Object after it is created? When you first add a cylinder, you have the option to change the number of vertices, etc, but once you do anything else in blender, it seems you no longer can edit those parameters.   Is there a setting anywhere or an add-on that allows these parameters to be edited later on? If not, how easy would such an addon/feature be to create for anyone reading this? Linear regression best polynomial (or better approach to use)? Any ideas on other polynomials I could successfully use for applying regression? My goal is a solution that has fit error strictly based on the noise. Is this possible since it is a bell-like curve? The tails can be long, short or non-existent. Am I looking for the impossible? Please note it has been a while since I have plunged this far into linear regression.   Anyway, my data points do not fit the $ax+bx^2+c$ polynomial well enough. I would like a replacement for this polynomial to apply regression (or different approach). In the following example, each point misses the fit curve by $20\%$ of the $Y$ range on average (of the data points). I looked at splines, but I do not know how to apply the regression since they look piece-wise.   Example $Y$ values (evenly spaced in $X$). It looks kind of like a bell curve. I would be applying 5 to 50 data points to determine the polynomial coefficients. Ultimately, I am interested in the best $X$ location for the peak based on the data points.     X      Y -40    -21142.1111111111 -30    -21330.1111111111 -20    -12036.1111111111 -10      7255.3888888889   0     32474.8888888889  10     32474.8888888889  20      9060.8888888889  30    -11628.1111111111  40    -15129.6111111111 In which situations is it OK to omit articles in short sentences? Recently, in many new online software I often see that developers omit articles in short sentences, especially on action buttons or tooltips.     For instance: "Add new task" (not "Add a new task"), "Create project" (not "Create a project"), but often in the same software I can see "Make a copy". What are situations it can be justified? I've searched websites, written to Mr. Barth and William Safire, scanned bookstore shelves, and buttonholed likely prospects in search of a grammar text that would address matters in the manner of the following, which is from John Barth's "The End of the Road".  If such a text exists, I'd be much obliged to learn of it:  " ... it gives a man a great sense of lucidity and well-being, if not downright formidability, to be able not only to say, but to understand perfectly, that predicate complements of infinitives of copulative verbs without expressed subjects go into the nominative case, whereas predicate complements of infinitives of copulative verbs with expressed subjects go into the objective case.  I made this observation to my assemblage of young scholars and concluded triumphantly, "I was thought to be he, but I thought John to be him."  Thank you. Transferring Money from India Using sObject.get() to fetch a field value from a related parent object I have a contact in a generic sObject in apex and while I'm able to easily get detail field values using   sObject.get('MyContactField__c')  I'm not able to get fields off the related parent object, and I'm sure the related field is in memory, based on the debug logs. This returns a runtime error:  sObject.get('Account.MyAccountField__c')  with the error     Invalid field Account.MyAccountField__c' for Contact   How do I get a field value off of a parent on a generic sObject? TikZ/PGF 3.0 datavisualization vs pgfplots To follow-up on a previous question , the current release of TikZ 3.0 has a flexible datavisualization engine that creates the same kind of plots as the more mature plotting package pgfplots.  What is the current recommendation for producing complete plots in LaTeX? How do I select text nodes with jQuery? I would like to get all descendant text nodes of an element, as a jQuery collection. What is the best way to do that? Proving that $-a=(-1)\cdot a$ As the title reveals, I want to prove (based on the axioms of field) that $$-a=(-1)\cdot a$$ I've been trying for a while now, but couldn't think of a way to do it and it got me thinking that maybe its does not require a proof, but it doesn't feel right. Any ideas? Do parts of a hash carry the properties of the entire hash? When I need to generate unique id's based on some information hashing is typical choice. However, sometimes that id needs to be of a particular size.  I've seen a lot of schemes (HMAC-MD5-96 in SSH, CGA in SeND for IPv6) that use a portion of a hash, so I'm thinking it might be alright to use it that way.    Which properties of a hash are preserved and which do not apply anymore?  Obviously, with less bits, the chance of collision goes up, but can I still rely on the partial hash for uniform character distribution?  What about the ?  I'm guessing that if a hash modifies the entire hash upon the smallest change to the input, that would imply that a portion of that hash would be equally well changed.  Am I thinking about this correctly?  Also, would these behaviors be different for different hashing algorithms? Multivariable limit - perhaps a trickier problem I am stuck on. I am trying to solve the following limit:  $\lim_{(x,y) \to (0,0)} \frac{x^4y^4}{(x^2 + y^4)^3}$  (This is a more challenging problem from Folland Calculus, it seems).  I am pretty sure this limit does not exist (however, this is just a guess, and I am not 100% sure.)  I am trying to approach via the paths y = mx and x = my but... they don't seem to work. I have tried simpler cases such as x = 0 and y = 0.   Any help appreciate. When should I load assets for optimal performance? I'm writing a game using LWJGL and Java, and was wondering if there were best practices for when to load resources.  I have seen examples that load all resources when initializing the game (XNA), ones that load the new resources needed for each level while referencing the already loaded assets again. apt install "*" method in Ubuntu 20.04 does not work How can I bake the cloth simulation into keyframed vertices or shape keyed vertices? I'm simulating a cloth. How can I bake the cloth simulation into keyframed vertices or shape keyed vertices? I can't seem to get these particular faces to take the UV Mapping. I selected the entire object, entered edit mode, hit U>Unwrap.   The rest of the mesh takes the uv wrapping, but not those faces for some reason.    It looks normal in solid mode.     Does anyone know what could be causing this? What are bitwise shift (bit-shift) operators and how do they work? I've been attempting to learn C in my spare time, and other languages (C#, Java, etc.) have the same concept (and often the same operators) ...   What I'm wondering is, at a core level, what does bit-shifting (&lt;&lt;, &gt;&gt;, &gt;&gt;&gt;) do, what problems can it help solve, and what gotchas lurk around the bend? In other words, an absolute beginner's guide to bit shifting in all its goodness.