I am bit confused about datums used to define a localised coordinate system for a specific area. Definitions say that, datum defines how a certain well-established point (i.e., reference point) on earth is located on a reference ellipsoid used to model that area. So, it establishes latitude and longitude of that reference point on earth with GPS or other means. My question now is, with respect to which reference frame are these latitude and longitude measured? is it always wrt earth-centric WGS84 or ITRS? So, when a textbook says, the coordinate of a NAD27 reference point is 39°13′26.686″ north latitude, 98°32′30.506″ west longitude, is it measuring these values from Equator and Greenwich respectively on physical earth surface or on a reference ellipsoid? How coordinates of this point was established before GPS was in place?  On the other hand, when GPS is used to establish the coordinate of a reference point, isn't it always measuring the lat. and long. on the ellipsoid corresponding to WGS84?  I haven't found any textbooks that explain it in a simple way.
What's the difference between a projection and a datum?
Fullscreen YouTube video crash How to determine $\int x^2 e^{-x^2}\mathrm dx$? Custom Gmail labels sort I want to sort the labels in my own order instead of the default abc order, so that, for example, the label named bills should come up first.  Any way to do that? I want to untriangulate every object in my scene with this script:  import bpy  for ob in bpy.data.objects:     bpy.ops.mesh.tris_convert_to_quads(limit=0.9, uvs=False, vcols=False, sharp=False, materials=False)   But it doesn't work in object mode, any ideas on how I can get it working? Remove array element based on object property What is wrong with code snippets/blocks on Stack Overflow? I wasn't following Meta Stack Overflow too closely so maybe something was changed that I'm not aware of. But each time I paste a snippet from a Python console I'm getting wrong formatting. What I'm doing wrong? It seems that &gt;&gt;&gt; is confusing for Stack Overflow. I've tried to escape it with backslashes, and it was working fine in preview but doesn't work after the question is rendered.  I was able to observe that problem on: recent Chrome (Windows, Mac), Safari 4 (Mac).  Here is  I wasn't able to make right.  Funny, I think the snippets are rendered just fine on Meta Stack Overflow. Here is one:  &gt;&gt;&gt; def throw(): raise Exception()  ...  &gt;&gt;&gt; a=1 &gt;&gt;&gt; a=throw() Traceback (most recent call last):   File "&lt;stdin&gt;", line 1, in &lt;module&gt;   File "&lt;stdin&gt;", line 1, in throw Exception &gt;&gt;&gt; a 1 Fibonacci numbers and proof by induction Consider the Fibonacci numbers $F(0) = 0; F(1)=1; F(n) = F(n-1) + F(n-2)$.  Prove by induction that for all $n&gt;0$,  $$F(n-1)\cdot F(n+1)- F(n)^2 = (-1)^n$$  I assume $P(n)$ is true and try to show $P(n+1)$ is true, but I got stuck with the algebra. How do we reach $P(n+1)$ from $P(n)$? Also, strong induction may be used instead. Why are these estimates to the German tank problem different? Suppose that I observe $k=4$ tanks with serial numbers $2,6,7,14$.   What is the best estimate for the total number of tanks $n$?   I assume the observations are drawn from a discrete uniform distribution with the interval $[1,n]$. I know that for a $[0,1]$ interval the expected maximum draw $m$ for $k$ draws is  $1 - (1/(1+k))$. So I estimate $\frac {k}{k+1}$$(n-1)≈$ $m$, rearranged so $n≈$ $\frac {k+1 }{k}$$m+1$.  But the frequentist estimate from  is defined as:  $n ≈ m-1 + $$\frac {m}{k}$  I suspect there is some flaw in the way I have extrapolated from one interval to another, but I would welcome an explanation of why I have gone wrong! Can I successfully bake previously-frozen bread dough? Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$ How can momentum but not energy be conserved in an inelastic collision? When is the past perfect exactly needed? I am trying to find the splitting field of $x^6+x^3+1$ over $\mathbb{Q}$.  Finding the roots of the polynomial is easy (substituting $x^3=t$ , finding the two roots of the polynomial in $t$ and then taking a 3-rd root from each one). The roots can be seen  [if there is a more elegant way of finding the roots it will be nice to hear]  Is is true the that the splitting field is $\mathbb{Q}((-1)^\frac{1}{9})$ ? I think so from the way the roots look, but I am unsure.  Also, I am having trouble finding the minimal polynomial of $(-1)^\frac{1}{9}$, it seems that it would be a polynomial of degree 9, but of course the degree can't be more than 6...can someone please help with this ? Friend was brainwashed by MLM-/ponzi investment scam. What can I do? Recently a friend of mine invited me to hear about “an interesting chance to simply earn money.” Basically we and other invited people drove to a meeting room where a speaker told us about a growing startup where you could invest money in a field where similar investments had an ROI of apparently 1000 times the investment in 6 years. Afterwards there was coffee and small talk together, during which they also indoctrinated people saying, they should avoid talking to people talking bad about the investment (or saying it is scam) because you can't gain money from them and they just want to destroy your business.  You earn money if you invest money and if you refer friends who invest money up to multiple levels. The more you invest yourself the greater percentage you earn for your referrals.  Since I had already seen other ponzi-/MLM-schemes and I am from the field it is based in, I recognized that there is no real product and it is a ponzi-/MLM-scheme. Later I found its name on the official scam warning list of multiple countries.  From what I understand, my friend has already invested multiple months or years worth of income; and is earning an amount of money through referrals that would mean scamming other people directly or indirectly through referrals for possibly several $100,000's per month to earn an additional bonus. He also wants to use his position as a respected member of multiple local youth groups and other community groups to get their members as referrals or in his words “…to give them the opportunity to also simply earn money.”  I tried to convince him that it is just a ponzi scam with my knowledge in this field but he answered with the indoctrinated speech “You don’t need to know the details if it makes you rich or use it. You also don't know how every detail of a smartphone works?”/“My sponsor already earned $x with this” or “If you don't believe in this, just stop talking about it to me and other people or do you want to ruin me, my business and my investments?.” So basically this means I can either make his investment worthless/let him lose everything (he also quit his job) or let him scam other people and motivate them to scam other people.  At the moment you can only withdraw small amounts of money out of it because the company invented some reason but you will be able to withdraw all of it “soon” (=most likely never).  What is the best way to resolve this situation (best meaning with lowest loss of money for everybody)?  Edit: The founders are known names in Ponzi schemes or convicted for crimes like fraudulent bankruptcy and many of their claims are technically impossible or proven to not exist with very high probability according to sites about ponzi schemes. But of course they say "Every bigger company has their scandals".  You can't trade the bought virtual coins outside the company and the only product you can buy can be bought anywhere else for less than 10% of the price without the logo.  When I met other friends they mentioned that they got invitations for the same meeting. I just stated to them that I already went to one and told them the name of the company (which was not stated on the invitation) and that I will not invest in it because there are official warnings that this is a scam. How to suppress scientific notation when printing float values? Here's my code:  x = 1.0 y = 100000.0     print x/y   My quotient displays as 1.00000e-05.  Is there any way to suppress scientific notation and make it display as 0.00001? I'm going to use the result as a string. CPU Emulation and locking to a specific clock speed If you had read my other , you'll know I've spent this weekend putting together a 6502 CPU emulator as a programming exercise.  The CPU emulator is mostly complete, and seems to be fairly accurate from my limited testing, however it is running incredibly fast, and I want to throttle it down to the actual clock speed of the machine.  My current test loop is this:      // Just loop infinitely.     while (1 == 1)     {                         CPU.ClockCyclesBeforeNext--;          if (CPU.ClockCyclesBeforeNext &lt;= 0)         {             // Find out how many clock cycles this instruction will take             CPU.ClockCyclesBeforeNext = CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].CpuCycles;              // Run the instruction             CPU.ExecuteInstruction(CPU.Memory[CPU.PC]);              // Debugging Info             CPU.DumpDebug();             Console.WriteLine(CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength);              // Move to next instruction             CPU.PC += 1 + CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength;                                                 }     }   As you can tell, each opcode takes a specific amount of time to complete, so I do not run the next instruction until I count down the CPU Cycle clock. This provides proper timing between opcodes, its just that the entire thing runs way to fast.  The targeted CPU speed is 1.79mhz, however I'd like whatever solution to the clock issue to keep the speed at 1.79mhz even as I add complexity, so I don't have to adjust it up.  Any ideas? Are continuous self-bijections of connected spaces homeomorphisms? I hope this doesn't turn out to be a silly question.  There are lots of nice examples of continuous bijections $X\to Y$ between topological spaces that are not homeomorphisms.  But in the examples I know, either $X$ and $Y$ are not homeomorphic to one another, or they are (homeomorphic) disconnected spaces.    My Question: Is there a connected topological space $X$ and a continuous bijection $X\to X$ that is not a homeomorphism?    For the record, my example of a continuous bijection $X\to X$ that is not a homeomorphism is the following.  Roughly, the idea is to find an ordered family of topologies $\tau_i$ ( $i\in \mathbb Z$) on a set $S$ and use the shift map to create a continuous bijection from $\coprod_{i\in \mathbb Z} (S, \tau_i)$ to itself.  Let $S = \mathbb{Z} \coprod \mathbb Z$.  The topology $\tau_i$ is as follows: if $i&lt;0$, then the left-hand copy of $\mathbb Z$ is topologized as the disjoint union of the discrete topology on $[-n, n]$ and the indiscrete topology on its complement, while the right-hand copy of $\mathbb Z$ is indiscrete.  The space $(S, \tau_0)$ is then indiscrete.  For $i&gt;0$, the left-hand copy of $\mathbb Z$ is indiscrete, while the right-hand copy is the disjoint union of the indiscrete topology on $[-n, n]$ with the discrete topology on its complement.  Now the map $\coprod_{i\in \mathbb Z} (S, \tau_i)\to \coprod_{i\in \mathbb Z} (S, \tau_i)$ sending $(S, \tau_i) \to (S, \tau_{i+1})$ by the identity map of $S$ is a continuous bijection, but not a homeomorphism. How can I import Opera bookmarks into Chrome? What does $\mathbb{R} \setminus S$ mean? What does $\mathbb{R}\setminus S$ mean? I am not getting it what it actually means. I have found it manywhere in real-analysis like in the definition of boundary points of a set. Can anyone tell me what it means really? In eevee, shadows are clipped by camera distance