I am reading the book . I have a doubt in the topic "The field as representation". In this topic authors give the example of gravitational force represented as a field. In the following image the small circle represents an attracting body(say sun) and the lines are the well known lines of force of the gravitational field.  It is said that the density of the lines of force in space shows how the force varies with the distance. Let us consider a finite volume $\Delta V$  in the vicinity of sun. Now the number of lines of force passing through this is finite but there are infinite points in this $\Delta V$ volume. $1.$Is there any gravitational force acting on those points through which no line of force passes. $2.$ If the gravitational force acts on all the points contained in $\Delta V$ shouldn't there be infinite lines of forces passing through $\Delta V$.    $3.$ If it is supposed that there are really infinite lines of force passing thru $\Delta V$ then how to decide the density of no of lines won't it be infinite.      Please cite some canonical references which explains the 3 different points I've mentioned in your answer.    Thank you.
When we're dealing with problems in electrostatics (especially when we use Gauss' law) we often refer to the density of electric , which is inversely proportional to the radius in the case of a single point charge (all field lines are directed radially).   My question may sound dumb, despite the fact that this concept is quite intuitive, but if you think about it there is actually an infinite amount of field lines which we can draw everywhere (one through every point), so speaking of an area where field lines are more "dense" or "sparse" doesn't make much sense to me.  With this in mind, why can we still use such a concept? Why does it really work?
Given an instance of System.Reflection.Assembly. Splitting raster into smaller chunks using GDAL? I have a raster (USGS DEM actually) and I need to split it up into smaller chunks like the image below shows. That was accomplished in ArcGIS 10.0 using the Split Raster tool. I would like a FOSS method to do this. I've looked at GDAL, thinking surely it would do it (somehow with gdal_translate), but can't find anything. Ultimately, I'd like to be able to take the raster and say how large (4KM by 4KM chunks) I would like it split up into. PHP: Right way to declare variable before use in loop I have a variable that is built in loop. Something like:  $str = ""; for($i = 0; $i &lt; 10; $i++) $str .= "something";   If $str = "" is ommitted, I get undefined variable notice, but I thought php auto-declare a variable the first time it sees undeclared one?  How do I do this right? 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Comment on Duplicate Reference: Why would this be marked duplicate when it was asked years prior to the question referenced as a duplicate?  I also believe the question, detail, and response is much better than the referenced question.  I've been a C++ programmer for quite a while but I'm new to Java and new to Eclipse.  I want to use the  to visualize some data I'm working with.  This code is organized like this:  ./com ./com/touchgraph ./com/touchgraph/graphlayout ./com/touchgraph/graphlayout/Edge.java ./com/touchgraph/graphlayout/GLPanel.java ./com/touchgraph/graphlayout/graphelements ./com/touchgraph/graphlayout/graphelements/GESUtils.java ./com/touchgraph/graphlayout/graphelements/GraphEltSet.java ./com/touchgraph/graphlayout/graphelements/ImmutableGraphEltSet.java ./com/touchgraph/graphlayout/graphelements/Locality.java ./com/touchgraph/graphlayout/graphelements/TGForEachEdge.java ./com/touchgraph/graphlayout/graphelements/TGForEachNode.java ./com/touchgraph/graphlayout/graphelements/TGForEachNodePair.java ./com/touchgraph/graphlayout/graphelements/TGNodeQueue.java ./com/touchgraph/graphlayout/graphelements/VisibleLocality.java ./com/touchgraph/graphlayout/GraphLayoutApplet.java ./com/touchgraph/graphlayout/GraphListener.java ./com/touchgraph/graphlayout/interaction ./com/touchgraph/graphlayout/interaction/DragAddUI.java ./com/touchgraph/graphlayout/interaction/DragMultiselectUI.java ./com/touchgraph/graphlayout/interaction/DragNodeUI.java ./com/touchgraph/graphlayout/interaction/GLEditUI.java ./com/touchgraph/graphlayout/interaction/GLNavigateUI.java ./com/touchgraph/graphlayout/interaction/HVRotateDragUI.java ./com/touchgraph/graphlayout/interaction/HVScroll.java ./com/touchgraph/graphlayout/interaction/HyperScroll.java ./com/touchgraph/graphlayout/interaction/LocalityScroll.java ./com/touchgraph/graphlayout/interaction/RotateScroll.java ./com/touchgraph/graphlayout/interaction/TGAbstractClickUI.java ./com/touchgraph/graphlayout/interaction/TGAbstractDragUI.java ./com/touchgraph/graphlayout/interaction/TGAbstractMouseMotionUI.java ./com/touchgraph/graphlayout/interaction/TGAbstractMousePausedUI.java ./com/touchgraph/graphlayout/interaction/TGSelfDeactivatingUI.java ./com/touchgraph/graphlayout/interaction/TGUIManager.java ./com/touchgraph/graphlayout/interaction/TGUserInterface.java ./com/touchgraph/graphlayout/interaction/ZoomScroll.java ./com/touchgraph/graphlayout/LocalityUtils.java ./com/touchgraph/graphlayout/Node.java ./com/touchgraph/graphlayout/TGAbstractLens.java ./com/touchgraph/graphlayout/TGException.java ./com/touchgraph/graphlayout/TGLayout.java ./com/touchgraph/graphlayout/TGLensSet.java ./com/touchgraph/graphlayout/TGPaintListener.java ./com/touchgraph/graphlayout/TGPanel.java ./com/touchgraph/graphlayout/TGPoint2D.java ./com/touchgraph/graphlayout/TGScrollPane.java ./TG-APACHE-LICENSE.txt ./TGGL ReleaseNotes.txt ./TGGraphLayout.html ./TGGraphLayout.jar   How do I add this project in Eclipse and get it compiling and running quickly? $\mathbb{R}P^4$ and $\mathbb{R}P^6$ do not admit fields of tangent $2$-planes See the related question . 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