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. T

    Finding Fixed Points of a Mobius transformation

    Homework Statement Find all the fixed points to the following Mobius transformation. Homework Equations m(z) = (2z + 5)/(3z - 1) The Attempt at a Solution Aren't all fixed points going to map to themselves? So shouldn't it be solving for m(z) = z and coming up with roots of a quadratic...
  2. R

    Quadratic Formula (Equilibrium Points)

    Homework Statement The following is part of a solution to a problem about finding equiblirum points of a differential equation and sketching its bifurcation diagram http://img32.imageshack.us/img32/9194/63226925.jpg How did they get y= -1 \pm \sqrt{1- \mu}? Homework Equations The...
  3. J

    MHB Minimum degree of a polynomial passing through points

    If p(x) is a polynomial such that p(0)=5 ,p(1)=4 ,p(2)=9,p(3)=20 , the minimum degree it can have
  4. J

    Hydraulics problem - calculate pressure at different points

    Homework Statement Hey, stuck on this question in my hydraulics course: Question involves lubricating oil pumped around a large piece of machinery. Density of oil = 810 km/m3. Viscosity = 0.01 kg/m.s throughout the system. Flow rate is 0.140 Litres/sec Pipe diameter = 3mm Pressure...
  5. A

    Trying to prove dual of there are at least tree points on every line

    trying to prove dual of "there are at least tree points on every line" Hi, Assuming the propositions of incidence: (1) on any two distinct points is at least one line. (2) on any two distinct points is at most one line. (3) on any two distinct lines is at least one point. and the...
  6. R

    Fixed points of conjugate functions

    Homework Statement suppose f and g are conjugate show that if p is an attractive fixed point of f(x), then h(p) is an attractive fixed point of g(x). Homework Equations f and g being conjugate means there exist continuous bijections h and h^-1 so that h(f(x)) = g(h(x)) a point p...
  7. S

    Calulate probability of points allocation

    Hi, First time posting so be gentle :) I have a website and on the website I calculate popularity of objects over time. One of the objects is called 'Store Category' - a store has one or more categories. I.e. the store Easyjet, has categories 'Flights', 'Hotels' etc. In order to apply...
  8. Z

    Resistance in an octahedron between two points.

    Homework Statement Twelve identical wires, each with resistance 1.0 ohms, are linked together to form a octahedron (see figure). What is the resistance between corners E and F? http://etc.usf.edu/clipart/65700/65732/65732_octahedron_md.gif Homework Equations I assume: Ohms Law...
  9. B

    Can Baryon Acoustic Oscillation Accurately Measure the Universe's Expansion?

    Last week I read this article in Science Daily about BOSS and its recent most accurate measurements of the universe to date. http://www.sciencedaily.com/releases/2012/03/120330081844.htm In describing the experiment to measuring the accelerating expansion of the universe...
  10. M

    Finding the local extrema or saddle points of a function

    Homework Statement f(x,y)=5xy-7x^2+3x-6y+2 [b]2. Homework Equations (f_xx)(f_yy)-(f_xy)^2 the hessian or discriminant of f The Attempt at a Solution i arrived at a solution but i don't think its correct, and the answer isn't in the back of the book, so i just wanted to ask if i did...
  11. D

    Numerical integration, use given random distribution as integration points

    Hi folks, I need to evaluate (numerically) a multi-dimensional integral of the form \int_A f(x) dx. Now in my application, I already have points inside the domain A which are distributed like \frac{f(x)}{\int_A f(x) dx}. So I hoped I could use these random points in some importance sampling...
  12. Z

    Program to solve for a formula given a set of pairs of points?

    Hi, I'm look for a program that can solve for a general function when given a set of pairs of points? Does anything like that exist? Thanks.
  13. M

    If f:R->R is continuous on a dense set of points in R, then f is continuous on R.

    Homework Statement T or F, If f:ℝ→ℝ is continuous on a dense set of points in ℝ, then f is continuous on ℝ. Homework Equations definition of continuity using sequences, maybe? The Attempt at a Solution false. Take f(x)= {1 if x\in Q(rational numbers) and 0 if x\in...
  14. L

    Finding the equation of a plane passing through 3 points

    Homework Statement Find the equation of the plane passing through point A(2,1,0), B(3,-1,5) and C(2,2,1) Homework Equations Um..I don't know? The Attempt at a Solution Vector AB=(3 -1 5)^T-(2 1 0)^T=(1 -2 5)^T Vector AC=(2 2 1)^T-(2 1 0)^T=(0 1 1)^T perpendicular...
  15. S

    Finding increasing/decreasing intervals of an equation using critical points?

    Homework Statement Hi I have an equation as follows: f(x) = (2x-2.3)/(2x-5.29)^2 what i got for the derivative was: f'(x) = (-1.38-4x)/(2x-5.29)^3 Homework Equations f(x) = (2x-2.3)/(2x-5.29)^2 f'(x) = (-1.38-4x)/(2x-5.29)^3 The Attempt at a Solution what i got for the...
  16. I

    MHB Probability of Consecutive Data Points Rising and Falling in a Saw-tooth Pattern

    What is the correct way to calculate the probability of a given number of consecutive data points forming a saw-tooth pattern? The magnitudes of the rise or fall (the size of the moutain and valleys) are not material. The only requirement is that each set of three consecutive data points...
  17. K

    Find All local maxima and minima and all saddle points of the function

    Homework Statement ## f\left( x,y\right) =x^{2}-4xy+6x-8y+2y^{2}+10 ## ## f_{x}=2x-4y+6=0 ## ## f_{y}=-4x-8+4y=0 ## ## f_{y}=-4\left( x-y+2\right) ## -2=x-y, then solving fx and using this equality ## f_{x}=0=2\left( x-2y+3\right) =0 ## 2(-2 -y+3)=0 2(1-y)=0 y=1, then pluggin...
  18. A

    Level Sets and Degenerate Critical Points

    How would one show that if there is a number c for which g'(c)=0, then every point on the level set {(x,y)|H(x,y)=c} is a degenerate critical point of f? I know that the question may seem vague, but this is the question as it was given to me by my professor. It is something to think about...
  19. T

    Calculating Speed Along Sides of Right Angle at Intersection with Ruler

    Homework Statement A right-angle is drawn on a sheet of paper. A ruler , which always remains perpendicular to the bisectrix of this angle moves over the paper with a speed 10cm/sec. The ends of the ruler intersect the sides of the angle. What are the speeds along the sides of the angle of...
  20. A

    Distribution of Euclidean Distance btwn 2 Non-Centered Points in 2D

    I would like to know the distribution of z as the euclidean distance between 2 points which are not centred in the origin. If I assume 2 points in the 2D plane A(Xa,Ya) and B(Xb,Yb), where the Xa~N(xa,s^2), Xb~N(xb,s^2), Ya~N(ya,s^2), Yb~N(yb,s^2), then the distance between A and B, would be...
  21. P

    MHB Exploring Chebyshev Equation's Singular Points and Regularity

    I have computed the singular points of Chebyshev equation to be x= 1, -1. What is the best way to find whether they are regular? Thanks.
  22. J

    Limit of critical points of algebraic functions

    Hi guys, I have questions about algebraic functions and not sure where to ask. Hope it's ok here. Given the algebraic function f(z,w)=a_0(z)+a_1(z)w+\cdots+a_n(z)w^n=0 I recall seeing a reference that stated as n increases, the critical points of the function migrate to the unit circle or...
  23. S

    Effects of soluble impurities boiling and melting points

    In my textbook, it says that impurities lower the melting point and increase the boiling point. But is this only true if the boiling point of the impurity is greater than the boiling point of the solvent, and the melting point is greater than of the solvent too? So essentially, if greater...
  24. GreenGoblin

    MHB Extrema points, function of three variable

    "Show that if a>b>c>0, then the function $f(x,y,z) = (ax^{2} + by^{2} + cz^{2})e^{-x^{2}-y^{2}-z^{2}}$ has two local maxima, one local minima, and four saddle points"
  25. S

    Points of action for thrust and drag forces and lift-drag ratio

    Hi, Can anyone help explaining the points of action of drag and thrust forces on an aeroplane in flight and also the realtionship between Lift-Drag ration and wing configuration?! Any help would be great!
  26. E

    Finding out if work is done with between two points with same electric potential

    if two points have the same electric potential, is it true that no work is required to move a test charge from one point to the other? Does that mean that no force is required, as well?
  27. C

    Question about isolated points.

    Homework Statement If I just had the set containing \pi on the real line. So this is an isolated point. Is this set closed? The Attempt at a Solution I think this set is closed because it contains its limit points, because it only has one point. Am i thinking about this correctly?
  28. E

    Determine equation given 3 points and 2 lines

    Homework Statement Two coplanar lines l1 and l2 are perpendicular to each other, l1 passes through the points (-3,2,3) and (-8,10,6). Find the equation for l2 if it passes through the point (7,49,25) Homework Equations The Attempt at a Solution determine the equation of l1 and use...
  29. R

    Infinite set of points on a line.

    If a line segment of size L, is made up of an infinite amount of points. Then divided into half, and then half again, divided into half to infinity, would this mean that the resulting line segment is a point made up of an infinite amount of points? Or would it be ∞/∞?
  30. W

    What do points on the manifold correspond to in reality?

    In SR the points in Minkowski space correspond to events. I recently read in a GR lecture note that the points on the manifold do NOT correspond to events like in SR (the author even says the points don't have a direct physical meaning). So what do they represent then? And if I continuously...
  31. A

    MATLAB 2D discrete function minimization if extreme points are known, using Matlab

    Hello everyone. I would like to hear some suggestions on minimizing a function. I have discrete 2D function (a grid, where each (x,y) point have some value), where I know only extreme points (more specifically - ridges. http://en.wikipedia.org/wiki/Ridge_detection). I want to reconstruct...
  32. K

    Visually attractive Mandelbrot zoom points

    Hi, I have been working on some Mandelbrot wallpapers for some time but have so far only visualized the whole set i.e. no zooming. I think that it could be nice with wallpapers visualizing a zoomed in part of the border of the set. Does anyone know coordinates to interesting places for zooming...
  33. O

    Calculus problem find the equation of the line given two points

    Consider the curve f(x) = 1/x Consider two points on f(x): Pa and Qa, where the x-coordinate of Pa is a, and the x-coordinate of Qa is a+1. Let La be the line connecting Pa and Qa 1.) Find the equation for La 2.) Find a formula that expresses A(a) = the area between f(x) and La 3.) Determine...
  34. J

    Existence of a limit point implies existence of inifintely many limit points?

    Homework Statement Prove the following statement is true or not: the statement: Let (X,d) be a non-empty metric space and A is a non-empty subset of X. Then if A' is not empty, then A' is infinte. Homework Equations Definition of limit point and its negation. The Attempt at a...
  35. M

    The time it takes this thing to travel across 3 points

    Hey! I have a problem that I have no clue how to solve. So I was hoping you guys could help me. I'm not from an English speaking country so I apologize. Homework Statement A thing is made to travel in water and on land. In water it travels with 20 m/s speed but on land with 25m/s speed. The...
  36. R

    Critical points (will be a function of beta and delta)

    Homework Statement Find the critical points where \alpha = 1. dv/dt = v2 + \alphav - u + \delta [I will call this (1)] du/dt = \betav - u [call this (2)] For what values of \beta and \delta are there no critical points? Homework Equations The Attempt at a Solution So...
  37. H

    Calculate Ellipse based on 4 points

    I need to move an object based on 100 images rotating. The object needs to move in a path that is forming an ellipse when I'm rotating the image based on my gestures. I have 4 points, 2 pairs of opposite points on X/Y axis, on the ellipse but how do I calculate the rest of the points so that...
  38. K

    Julia Sets: Periodic and Non-Periodic Points Explained

    I'm a little bewildered when reading about these Julia sets. From the definition a Julia set is the closure of all repelling periodic points of a complex map f. However I read that a Julia set always contain periodic and non-periodic points. Wasn't the definition including only periodic points...
  39. 9

    Find points of inflection from f''(x) = 12x + 18? A bit confused

    Homework Statement In my book it specifically asks to "find the points of inflection" of f (x) = 2x^3 + 9x^2 - 24x - 10. Homework Equations f (x) = 2x^3 + 9x^2 - 24x - 10 f'(x) = 6x^2 + 18x - 24 f''(x) = 12x + 18. The Attempt at a Solution What I don't get is why it asks for pointS...
  40. S

    Existence of a root between 2 given points

    Homework Statement Show that there exists one root int (0,2) of the following function: f(x)=(1-x^2)^2-√((1-x^2)*(1-1/2*x^2)) Homework Equations The Attempt at a Solution I first found: f(0)=0 and f(2)=7.268 But, i don't know what to do now. I'm not sure if it has...
  41. S

    Velocity of points on a moving wheel relative to the ground

    Homework Statement A wheel with a radius 50 cm is rolling along the ground at 10m/s[E]. That is, the centre point of the wheel is moving at 10 m/s [E]. - What are the velocities of the top, bottom, front, and back points of the wheel, relative to its center? - What are the velocities...
  42. P

    Electric potential from electric field at 2 points

    Homework Statement i have a sphere with center at origin that is partially empty inside with a non-uniform charge. i have 2 arbitrary points outside the sphere. find the difference in potential between the 2 points.Homework Equations The Attempt at a Solution 1) find total charge of sphere 2)...
  43. P

    Differentiation and Stationary Points

    Hi, Q: By investigating the stationary points of f(x)= x3+3x2+6x-30 and sketching the curve y=f(x) show that the equation f(x)=0 has only one real solution. A: Well, I don't understand how I should use both. Plotting the graph, I can clearly spot a solution: x = 1.9319548 I know how to...
  44. H

    How can extrema points be used to prove mathematical inequalities?

    I'm reading a math book and found a couple of proofs I can't do. 1. Given x \in R^n, a \in R, \sum\limits_{i=1}^n{x_i}=na, prove that \sum\limits_{i \in A}\prod\limits_{j = 1}^k {x_{i_j}} \leq \binom{k}{n}a^k where A = \{i \in \{1, 2, ... n\}^k : i_1 < i_2 < ... < i_k\} which essentially...
  45. F

    Questions on speed of an object from different reference points.

    This thought experiment involves two people named Person-A and Person-B. Person-A fires a gun from a car which is traveling at 60mph. Imagine that the bullet travels at a constant speed of 300mph for some time, assuming that the air friction is ignored. Person-B is stationary observing the...
  46. D

    Lagrangian points in circular restricted three-body problem

    QUESTION: In the circular restricted 3-body problem, if we consider motion confined to the x-y plane and adopt units such that G(m1 + m2) = 1 [m1 and m2 are the masses of the two heavy bodies], the semimajor axis of the relative orbit of the massive bodies = 1, and n = 1 (n is mean motion...
  47. G

    Functions: instead of plotting points, can you move planes?

    This is a question that has been burning for some time, I have been wondering, instead of plotting the different points of a function onto a steady x and y axis, is it possible to have a single point (at the origin) and have the planes move instead. The space moving around the point. When I...
  48. M

    Finding the intersection points of the two lines in space

    given the lines in space L1 : x = 2t + 1, y = 3t + 2, z = 4t + 3 L2 : x = s + 2, y = 2s + 4, z = -4s – 1 Find the point of intersection of L1 and L2. How do i solve this?
  49. S

    Rolles Theorem, showing two distinct points.

    Have the following question and just wondering if my solution is correct Let g(x)= x^5+3x-1. Show that there are no distinct points x_1, x_2 in R such that g(x_1)=g(x_2). Proof by contradiction. Assume we have two solution x_1<x_2 in ℝ, i,e g(x_1)+g(x_2)=0, since g is differentiable on...
  50. Z

    Sequences, sets and cluster points

    Hello all, I am having trouble with a homework problem. The problem is as such: Let a = {zn = (xn,yn) be a subset of ℝ2 and zn be a sequence in ℝ2 such that xn ≠ xm and yn ≠ ym for n≠m. Let Ax and Ay be the projections onto the x and y-axis (i.e. Ax = {xn} and Ay = {yn}. Assume that the...
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