What is Points: Definition and 1000 Discussions

The Fourteen Points was a statement of principles for peace that was to be used for peace negotiations in order to end World War I. The principles were outlined in a January 8, 1918 speech on war aims and peace terms to the United States Congress by President Woodrow Wilson. However, his main Allied colleagues (Georges Clemenceau of France, David Lloyd George of the United Kingdom, and Vittorio Orlando of Italy) were skeptical of the applicability of Wilsonian idealism.The United States had joined the Triple Entente in fighting the Central Powers on April 6, 1917. Its entry into the war had in part been due to Germany's resumption of submarine warfare against merchant ships trading with France and Britain and also the interception of the Zimmermann Telegram. However, Wilson wanted to avoid the United States' involvement in the long-standing European tensions between the great powers; if America was going to fight, he wanted to try to separate that participation in the war from nationalistic disputes or ambitions. The need for moral aims was made more important when, after the fall of the Russian government, the Bolsheviks disclosed secret treaties made between the Allies. Wilson's speech also responded to Vladimir Lenin's Decree on Peace of November 1917, immediately after the October Revolution in 1917.The speech made by Wilson took many domestic progressive ideas and translated them into foreign policy (free trade, open agreements, democracy and self-determination). Three days earlier United Kingdom Prime Minister Lloyd George had made a speech setting out the UK's war aims which bore some similarity to Wilson's speech but which proposed reparations be paid by the Central Powers and which was more vague in its promises to the non-Turkish subjects of the Ottoman Empire. The Fourteen Points in the speech were based on the research of the Inquiry, a team of about 150 advisers led by foreign-policy adviser Edward M. House, into the topics likely to arise in the anticipated peace conference.

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  1. S

    Critical points of differential equation

    Homework Statement Determine the location and type of all critical points of the given equations and sketch the phase portrait y"+cosy=0 The Attempt at a Solution I've done some like this before but they were all systems of equations. I'm actually not sure how to do the...
  2. C

    Resolution of points by human eye

    I'm trying to teach myself optics from Frances Sears' book Optics from 1949. I'm attempting every problem, and there are answers to the odd ones in the back. I've gotten a lot of wrong answers and don't know why, had a few I just couldn't even see how to start, and at this point, I'm seeing...
  3. M

    Plotting Points on a Graph (4, 0°) and (3, 27°)

    Homework Statement I was wondering if you could help me on how to draw these on a graph (4, 0°) and (3, 27°) The Attempt at a Solution Just a hint, Please
  4. W

    What would happen if you try to fit 'n' degree polynomial to (n+1) data points?

    I couldn't get these lines from my book. I will reproduce it here. Warning: In step 1, if you use computer to fit a polynomial to the data , it could lead to disaster. For example, consider fitting a sixth degree polynomial to the seven data points, or, an (n-1) degree polynomial to n...
  5. D

    Points that a curve's normal line intersects

    Homework Statement The line that is normal to the curve x2+2xy-3y2=0 at (5,5) intersects the curve at what other point? 2. The attempt at a solution I differentiated the equation, found the slope of the curve at that point, and I then found the equations for the tangent line and normal...
  6. T

    Quick question about use of the Hessain for critical points

    So I am solving for the critical points of x3-3x-y2+9y+z2 I've found the critical points and I'm just evaluating them in the Hessain. Now I computed the eigenvalues for the hessian, but one of my 2nd order derivatives was a constant. So my hessian looked like this (it was diagonal, so I'm...
  7. A

    Mathematical Iteration for Alignment of 4 Points

    What is the mathematical equation or algorithm for alignment of four points in cartesian coordinates (X & Y). Say, we have 4 nominal points (Xn & Yn), and another 4 measured points (Xm & Ym)?. After alignment, what are the new locations of the measured points (Xmn & Ymn)?.
  8. H

    Numerical intergration of a set of measured data points

    Hi, I have faced the following question. In our lab we perform different measurements on Transistors. We program a scope and that controls the tests. For one of our tests we would like to calculate the total charge Q. Mathematically this is given by Q=∫ dt i(t), where i(t) is given by i(t)...
  9. L

    Help with a derivative and solving for Critical points

    I have the equation (x^2)/(sqrt(x+1)) This one has been stumping me, not sure how to reduce the derivative properly much less solve for 0. I get it down to this using the quotient rule: ((x+1)^(1/2)*2x - x^2*1/2(x+1)^(-1/2)) / (x+1) Just started learning derivative a few weeks ago...
  10. S

    Fitting points to skewed sinusoids

    Fitting points to "skewed" sinusoids Hello, I have a problem related to least square fit of data. Let me start from a step back. I have a set of points, given as x-y coordinates. x represents an angle and y the corresponding value of a function. I am fitting sinusoids to those data points...
  11. D

    How can I identify TRIM points in the Brillioun zone?

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  12. C

    Points of concurrency and sets of parallel lines

    My question is mainly concerned with discovering the allowable set of "configurations" of the given problem: We have a two-dimensional board composed of three sets (of infinite size) of parallel lines \P_1, \P_2, \P_3, where the lines in \P_2 form a 60 degree angle with lines in \P_3 and \P_1...
  13. I

    Why is the electric field strong in sharp points?

    Why is the electric field strong in sharp points?? There is a question in my book regarding the intensity of the electric field near a sharp surface in a conductor. There is a hint which says that it will be helpful to examine the field lines near those sharp surfaces. This is from my...
  14. N

    The singular points on f = x^2 y - x y on a plane

    Let f(x,y) = x^2 y - xy = x(x-1)y be a polynomial in k[x,y]. I am looking for the singular subset of this function. Taking the partials, we obtain f_x = 2xy - y f_y = x^2 - x. In order to find the singular subset, both partials (with respect to x and with respect to y) must vanish. So...
  15. fluidistic

    Stability of 2 critical points in a system of DE's

    Homework Statement Basically I found the following system of DE's: \frac{dx}{dt}=y \frac{dy}{dt}=-\frac{g}{l} \sin x - \frac{cy}{ml}. (Damped pendulum) I'm asked to analize the stability of the critical points x=0, y=0 and x=\pi, y=0. Using intuition the first point is asymptotically stable...
  16. C

    Model a rigid body made of two points linked by a rigid bar

    Hi all! I need help..:) I need to model the dynamic of this system: I'm in the plane (2-dimensions). There are two points (with m1 and m2 masses) free to move with different speed vectors (in module and direction). At some point, when the distance between them is d, the two points...
  17. F

    Parametrization of a line formed by 3 points

    Homework Statement Find a parametrization of the equation of the line formed by the points A, B, and P. A(2,-1,3) B(4,3,1) P(3,1,2)Homework Equations x=x_0+v_1*t y=y_0+v_2*t z=z_0+v_3*tThe Attempt at a Solution Alright, so, I've already determined that P is equidistant from the points A and...
  18. J

    Baby rudin condensation points

    1st part of Exercise #27 is: Define a point p in a metric space X to be a condensation point of a set E in X if every neighborhood of p contains uncountably many points of E. Suppose E is in R^k, E is uncountable and let P be the set of all condensation points of E. Prove P is perfect...
  19. E

    Finding polar coordinates of polar points

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  20. R

    Stargazing What creates the star points in telescope pictures of stars?

    what creates the "star points" in telescope pictures of stars? it's a basic question. e.g. see this hi-rez Hubble Deep Space pic: http://upload.wikimedia.org/wikipedia/commons/9/9b/Hs-2004-07-a-full_jpgNR.jpg i count about three bright objects with pointy cross-like projections from...
  21. I

    Critical points of multivariable equations

    Homework Statement Find all critical points of u(x,y)=(x-y)(x^2+y^2-1) Homework Equations - The Attempt at a Solution Partial differentials: ux=3x^2+y^2-1-2xy=0 uy=-x^2-3y^2+2xy+1=0 I know the critical points are the solutions to the above two equations. But how do...
  22. H

    Critical points with multiple variables

    Homework Statement Locate and classify the critical points of f(x,y) = (x-y)(xy-1). Homework Equations The Attempt at a Solution I found the partial derivatives with respect to x and y and I got: ∂f/∂x = -y2+2xy-1 ∂f/∂y = x2-2xy+1 After setting them both equal to zero I can't...
  23. K

    Find Points C Along A(1, -1, 2) to B(2, 0, 1) Line

    Homework Statement Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vectors llACll= 2 llBCll Homework Equations Not sure. The Attempt at a Solution I found the equation of the line for vector AB: (1,2,-1) +t(2,0,1) Then found the scalar equation...
  24. S

    Why Does Substituting Into y^2 = 16x Yield t = 0?

    The point P(4t^2, 8t) lies on the parabola C with equation y^2 = 16x. The point P also lies on the rectangular hyperbola H with equation xy = 4 a) Find the value of t, and hence find the co-ords of P. working: so x = 4t^2 and y = 8t i sub these into xy = 4 and get t = 1/2 and can then...
  25. N

    Potential of two points how are they same?

    Homework Statement I am confused here . Each wire is of resistance R How in this image E G and D are at the same potential and in this image How A and F and Dand G are equivalent? Homework Equations I don't think any equations will be used in solving this but I guess V =IR might be...
  26. N

    Confusion:collapsing 3 points with equal potential in a cubical resistor network

    Homework Statement The question is to find Equivalent resistance between opposite ends of a cubical resistor network . each resistor of resistance R . I am referring to this website here http://mathforum.org/library/drmath/view/65234.html I am halfway through it but I am stuck at a...
  27. G

    Gluing points of [0, 1] to get [0, 1]^2

    By Peano's space-filling curve, there exists a continuous map f: I -> I^2 whos image fills up the entire square I^2 (where I=[0, 1]). This can also be represented by gluing points of I together. Which points of I get glued together? I was looking at the proof of Peano's space-filling curve...
  28. W

    Finding the unknown points of a second triangle

    Homework Statement Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3). Homework Equations Center of a triangle: x = ax+bx+cx /3 y = ay+by+cy / 3 Magnitude = <a,b> , √(a^2+b^2) The Attempt at...
  29. F

    Regarding fixed points in finite groups of isometries

    There is a theorem for finite groups of isometries in a plane which says that there is a point in the plane fixed by every element in the group (theorem 6.4.7 in Algebra - M Artin). While the proof itself is fairly simple to understand, there is an unstated belief that this is the only point...
  30. C

    Mathematica How to label points in 3D Scatter Plot (Mathematica)

    Hi, I really need some help here. Right now I am plotting points on a 3D Scatter plot chart in Mathematica. I want to assign each of these points with a value which will be the label. Basically each point has 4 variable in the parameter. Its x,y,z cartesian coordinate position and the last...
  31. K

    FInd the Vector passing thru a point and parallel to two points in a plane

    Hi, i have three points A',B',C' and want to find a vector passing through B' and parallel to the other two points in the plane containing these 3 points. So this how i started, A'=(9,27,-0.6) B'=(12,27,-6) C'=(19,25,-8) I found the vector AB' and AC' first. A'B'= A'-B' A'C'=A'-C'...
  32. D

    Calc. 3 Determining whether points lie in a straight line

    Hey, how do I determine whether or not points lie in a straight line? Is there a symbolic approach to determining so? Or do I need to spatially visualize it? For instance, A(0,-5,5), B(1,-2,4), C(3,4,2) does lie in a straight line according to my book. Thanks!
  33. T

    Critical points of a Hyperbolic function

    Homework Statement I am trying to find the critical points of the following hyperbolic function: f(x) = a / (b + x) Homework Equations Critical points--> where f '(x) = 0 One of the points on the graph is a/2b The Attempt at a Solution I am not sure how to proceed with this...
  34. K

    Find and Classify the critical points of f(x,y)

    Homework Statement f(x,y)= 16(y^2) +(x^4) y + 4(x^2) + 4 My problem is recognizing which critical points to consider valuables. Homework Equations fxx, fyy, fxy, and second partials test. D=fxx(fyy)- (fxy)^2 The Attempt at a Solution I found: fx=0 4(x^3)y +8x=0 (x^2) y= -2...
  35. P

    Plate four points bending equation for a plate

    Hello, I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory. I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam. However I cannot apply the beam theory...
  36. N

    Vector proof - four points in space

    The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN. I'm not quite sure where to start. Could someone please help me?
  37. E

    Cartesian equation of the plane through the given points

    Homework Statement For each part, find the cartesian equation of the plane through the given points. (1,0,3), (2,-4,3),(4,-1,2) The Attempt at a Solution No attempt. Dunno how to do :(
  38. N

    Mathematica Mathematica: NIntegrate data points

    Hi I have a set of data points in units of (time, voltage), and they have the form of a Gaussian when I plot it. I would like to normalize my data set, i.e. find a factor C that I multiply on to the voltage-data such that the area is 1. However, is there a way to numerically integrate data...
  39. R

    Finding Fixed Points in a System of Equations

    Homework Statement http://img444.imageshack.us/img444/9288/51927159.jpg The Attempt at a Solution (a) I'm mostly stuck on this part because I keep getting a complex number: 3x+y = 0 so x=-y/3 Substituting this in the second equation: \frac{y^2}{9} +1 = 0 \therefore \ y = \sqrt{-9}...
  40. N

    Critical Points, intervals, local max/min help Calculus.

    Critical Points, intervals, local max/min help! Calculus. 1. I need help with a homework problem that I just cannot get right. It asks: Answer the following questions about the functions whos derivative is given below. f'(x) = (sinx +1)(2cosx +\sqrt{3} ), 0\leqx\leq2∏ a. what are the...
  41. H

    Proving gradient points in the direction of maximum increase

    How do we prove that the gradient points in the direction of the maximum increase? Would it be enough to simply state that the gradient is just the derivates of a function w.r.t all the variables a function depends upon. Since the derivative of a term w.r.t a certain variable gives the maximum...
  42. J

    IM forces-substances of increasing melting points

    Q.In which of the answers below are the substances listed in order of increasing melting point? a) Cl2 < CHF3 < H2O < CHCl3 < SiO2 b) Cl2 < CHCl3 < CHF3 < H2O < SiO2 c) Cl2 < CHF3 < CHCl3 < H2O < SiO2 d) Cl2 < H2O < CHF3 < CHCl3 < SiO2 e) SiO2 < H2O < CHCl3 < CHF3 < Cl2 How can we tell...
  43. H

    Show y = (1+x)/(1+x^2) has three inflection points

    Homework Statement We are given the curve y = (1+x)/(1+x^2) Homework Equations y' and y'' The Attempt at a Solution I know the inflection points of y are the local minimum and maximum of y'; this can also be restated as the critical points of y''. My attempt is to find the...
  44. B

    Use C-R eqns to determine points whose fn's are analytic

    Homework Statement Use the Cauchy Riemann equations to those points whose functions are analytic ##f(z)=x^2-y^2-x+iy(2x+1)## Homework Equations C-R eqn's ##u_x=v_y, u_y=-v_x, z(x,y)=x+i y## The Attempt at a Solution ##u(x,y)=x^2-y^2-x## ##v(x,y)=y(2x+1)##...
  45. D

    Fixed Points of analytic functions

    Hi, I am in honors track Complex Analysis, and I think I've reached my limit. We got this proof, and I don't know where to start. "We saw in class that a mobius transformation can have at most one fixed point (or else is the identity map), extend this idea to all analytic functions mapping...
  46. N

    Find the points closest to the origin

    Homework Statement Find the points x^2 + xy + y^2 = 2 that are closest to the origin.Homework Equations Distance FormulaThe Attempt at a Solution I have to first solve this without using Lagrange Multipliers. This is essentially an ellipse. So I first completed the square: 3/4\,{x}^{2}+...
  47. F

    Vertex of Fundamental Domains & Elliptic Points

    Dear Folks: Suppose \Gamma is a discrete subgroup of SL2(R), which acts on the upper half complex plane as Mobius transformation. F is its fundamental domain. If z is a vertex of F which does not lie on the extended real line ( that is R\bigcup\infty ) ,then must x be an elliptic point...
  48. A

    Finding equation of a circle given circumference and containing points.

    Homework Statement Find the equation of a circle if the circumference is 18∏ and contains the point (2, 8) The Attempt at a Solution I know I can find the radius by setting 18∏=2∏r. r=9. the equation of a circle is (x-h)2+(y-k)2=r2 So I have 92= (2-h)2+(8-k)2 which becomes...
  49. J

    Equal Distances Between N Points in R^n-1+ | Solving System of Equations

    Is there a theorem that states that n distinct points in R^n-1 or higher one can be separated in an equal distance as the distance is greater than 0? We know that 4 distinct points in R^2 cannot be positioned in an equal distance>0 but in R^3 it is possible as a pyramid shape. If there is...
  50. B

    Error Calculation in Multiplication of two measurement points

    Homework Statement Hi All, I have a problem in calculating the thickness of a coating material inside a tube. The tubes inside diameter is measured before and after coating. The coating thickness is calculated by substracting the diameters and dividing by two to get the thickness of the...
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