Triangle Definition and 1000 Threads

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted



△
A
B
C


{\displaystyle \triangle ABC}
.In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted.

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  1. P

    Equilateral triangle coulombs law problem

    [Homework Statement 1.) Three charges are placed 25 cm apart in an equilateral triangle. Q1 has a charge of -6.0 nC, q2 has a charge of 4.0 nC and q3 has a charge of 4.0 nC. what is the force on q2? q1 is the top point, q2 is the bottom left leaving q3 on the bottom right Homework...
  2. O

    Exploring Reverse Triangle Inequality Norms

    I'm interested in thing that are norms except for the fact that they satisfy the reverse triangle inequality ||x+y|| \geq ||x|| + ||y||. The obvious example is taking p-norms for 0<p<1. Does anyone know of others or if there's any theory developed on this topic?
  3. M

    Can You Solve Euler's Triangle Formula with Just the Distance (d)?

    Hi all I have a question concerning Euler's triangle formula, where the distance (d) between the incenter and circumcenter of a triangle is given as d2 = R(R-2r), with R being the circumradius and r the inradius. I suck at algebra and I need to know how to solve this if I only know the...
  4. B

    Triangle inequality metric space

    Homework Statement Let (X,\theta) be a metric space. Take K > 0 and define. \theta : X \cross X \rightarrow \real_{0}^{+}, (x,y)\rightarrow \frac{K\phi(x,y)}{1+K\phi(x,y)} Show that (X,\theta) is a metric space. Homework Equations can someone please check my triangle...
  5. D

    Finding the Correct Parameterization for Line Integral

    Homework Statement I'm attempting Q 3 from ch 16.4 of Stewart (p 1060). We are required to find the line integral where C is the triangle with vertices (0,0), (1,0) and (1,2). The line integral is Int xy dx + x^2*y^3 dy Homework Equations The Attempt at a Solution...
  6. A

    Transforming Triangle in 3 Space with z = 1-x-y

    I am trying to transform a triangle in 3 space with the constraint that z = 1-x-y. At this point I have the following transformation matrix A, and three vector equations: | a1 a2 a3 | A = | a4 a5 a6 | | a7 a8 a9 | A*x1 = k1*y1...
  7. M

    Calculating Hypotenuse with C++ Code

    i am trying to write a code that calculates the hypotenuse of a triangle... when i try to run it, i get a run time error. I'm not exactly sure what the problem is. #include <iostream> #include <cmath> using namespace std; void hypotenuse(double side1, double side2...
  8. M

    Three point charges in an equilateral triangle

    Homework Statement I had this exam question for a final exam and I was wondering if I got it right or not. There are three point charges +4q equally spaced apart at the tips of an equilateral triangle with distance .11m apart from each other. What is the magnitude of the electric field at the...
  9. Y

    Exploring Energy Transformations: From Potential to Kinetic and Beyond

    MY ATTEMPT: gPE to KE - Water in waterfall KE to gPE - Climbing mountain Strain to KE - Firing an arrow KE to Strain - Trebuchet being wound back Strain to gPE - ? gPE to Strain - ? It is the last 2 for which I really cannot think of instances in life - PLEASE help me out!
  10. A

    Does Bisecting Angle A in a 3-4-5 Triangle Divide It into Two Equal Areas?

    Given triangle ABC. And given that it’s a common 3-4-5 right triangle. (this still qualifies as a scalene) So AB = 4 BC = 3 AC = 5 is the hypotenuse If Angle A was bisected, do the two newly formed triangles have the same area? And would the bisecting line hit the midpoint of...
  11. K

    Electric Forces on Point Charge q in Triangle ABC

    Homework Statement Point charges Q, -2Q and 3Q are situated at the corners A, B and C respectively of an eqilateral triangle of side l, and another point charge q, of the same sign as Q, is placed at the centre of this triangle. What is the force acting on the charge q, and what is the angle...
  12. Z

    Right triangle problem,please check

    Right triangle problem,please check! Homework Statement In the figure,TN=NK, ST=12 and SN=\sqrt{69}.Find the length of TK. [PLAIN]http://img695.imageshack.us/img695/633/50042657.png Homework Equations Pythagorean Theorem The Attempt at a Solution Segment SN is the median of the...
  13. R

    Minimum area of a triangle with fixed incircle

    Homework Statement Consider an isosceles triangles with height x and a fixed incircle of radius R. Show that the minimum area of such triangle occurs when x = 3R Homework Equations None. The Attempt at a Solution Well, I know that have to express the area of the triangle in terms...
  14. C

    Can Geometry and Algebra Explain a Triangle's Romance with a Parabola?

    Homework Statement Here's the problem: refer to question no. 6 http://img1.uploadscreenshot.com/images/orig/5/12314183569-orig.jpg" Homework Equations I am not sure :S The Attempt at a Solution This, honestly, is a question which I have no clue how to go about... Thanks...
  15. L

    Which of the following must be true about the area A of the triangle?

    Homework Statement If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle? a. A is always increasing b. A is always decreasing c. A...
  16. Puma

    Are quarks really in isocoles triangle positions?

    I have not had any luck in finding out how much is known about the actual positions of quarks in protons and neutrons. I am confused by the brief snippets of information I have managed to find. First by the fact that an electron is fired at a nucleon and that its path can reveal the prescence...
  17. H

    The height of a triangle, given 2 vectors and the area

    Homework Statement Triangle ABC formed by two vectors a = ( 2, 10, 25 ) and b = ( 5, 4, -2 ) attached at a point A. The area of the triangle is (81 root 5) / 2 And I need to find the length of the height AM (AM perpendicular to BC and the point M belongs to the line BC). Don't know where to...
  18. H

    Area of triangle formed by 2 vectors

    Homework Statement I have a triangle ABC formed by vectors a = ( 2, 10, 25 ) and b = ( 5, 4, -2 ) attached at a point P. And I have to calculate the area of the triangle ABC. Homework Equations I'm pretty certain that I need to find the area of the parellogram and then half it. So I...
  19. S

    Is Triangle ABC a Right Triangle?

    Homework Statement Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)..is ABC a Right triangle Homework Equations The Attempt at a Solution I took the dot product of vertices A(4, 1, 7).B(-2, 1, 1), and it gives 0..but however I am a little confused, as...
  20. R

    Convert triangle vertices to double integral polar coordiantes

    Homework Statement integrate f(x,y) = sqrt(x^2+y^2) over triangle with vertices (0,0) (0,sqrt2) (sqrt 2, sqrt 2) Homework Equations x= rcosO, y = rsinO x^2+y^2=r^2 The Attempt at a Solution im supposed to use a double integral converted to polar coordinates, so i used...
  21. S

    How to solve Trignometry and Solution of Triangle questions

    On my school days it was very simple because I used to take whatever I've and keep solving and by some or other ways I get succeed answering it but now as we are bounded by very less time (nearly a minute) so now I'm facing very hard time. How you know in which direction you need to go. I can't...
  22. R

    Archimedes' rule that area of a parabola is 4/3 times an inscribed triangle

    Homework Statement Let ABC be a piece of a parabola. The point B is chosen such that the tangent to the parabola at B is parallel to the line AC. Archimedes proved the Area of parabola inside ABC is 4/3 times the triangle ABC. Prove this using calculus Homework Equations The integral...
  23. O

    Rock Climbing - American Death Triangle

    This is the first time I've ever been to this forum, so I'm hoping this is an appropriate place to post this. It's been a good amount of time since my college level physics courses and this rock climbing phenomenon has me stumped. There is a rock climbing anchor arrangement called the...
  24. K

    Help with finding the volume of a triangle using definite intergral

    Hi. I need some help for a test tomoorow on thi sone kind of problem: Homework Statement Set up and evaluate an intergral to find the olume of a cone of height 12 m and radius 3 m at teh open end. A fast replay would be really helpful.
  25. M

    Point charges in an equilateral triangle

    In an equilateral triangle a positive point charge +q is located at each of the vertices. If a 4th charge is added at the midpoint between one of the sides could this charge be such that the force on it would be zero?
  26. D

    Finding Sides of an Oblique Triangle with Altitudes

    Homework Statement how can i find the length of an oblique triangle given the 3 altitudes (the line drawn perpendicular from a point of the triangle to the opposite side). I have no idea on how to solve it. Homework Equations The Attempt at a Solution
  27. H

    Isosceles Triangle related rates problem

    Homework Statement A trough is 9 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 8 inches deep...
  28. F

    Proof of the Ratio Test and the Triangle Inequality

    Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...
  29. F

    Proof of the Ratio Test and the Triangle Inequality

    Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...
  30. Z

    Electric Potential in a triangle

    Homework Statement What is the electric potential at the point indicated with the dot in the figure? The dot is in the center of an equilateral triangle with sides of 3 cm. The top point is a +2 uC charge and the bottom points are both -1 uC charges. Homework Equations V= kq/r The...
  31. T

    Membrane locking and CST triangle

    I often read on books that linear triangles do not have membrane locking for large deformations of plates/shells. I completely don't understand how this is possible. If one uses the well-known CST, stretching is measured as the increase in length of each edge of the triangle. Then, in the limit...
  32. D

    Does a Scalene Triangle Exist? Proving Its Existence with a Simple Construction

    Homework Statement Prove that a scalene triangle exists Homework Equations The Attempt at a Solution I really don't know how to approach this proof... should I do a direct proof or maybe by contradiction? Any help would be great...
  33. B

    P-adic metric Strong triangle inequality

    Hi Guy's I was wondering If anyone new of a good link about the P-adic metric Strong triangle inequality. I am trying to constuct a proof to show that the p-adic is a metric space. Must the proof use the Strong triangle inequality ie d(a,c)\leq max{d(a,b),d(b,c)} or can it use the...
  34. A

    Perpendicular Bisector & Altitude of Triangle: A(4;2) B(11;6) C(-3;-1)

    The vertices of a triangle are A(4;2) ; B(11;6) ; C(-3;-1) What is the equation of the perpendicular bisector of side a? (i think -7x+14y=7) What is the equation of the altitude of side c? (i think -4x+7y=5) What is the intersection of the previous lines? i have no idea about this,please...
  35. D

    Cutting an Isosceles Triangle in Half

    Homework Statement Take an Isosceles triangle with a height of 10 and draw a line parallel to the base. How far from the top of the triangle does the drawn line have to be for the top half's area to equal the bottom half's area. Homework Equations The area of a triangle...
  36. M

    Understanding Triangle Inequality and applying it

    I was wondering if anyone knew of a text or website that has a very indepth explanation of the triangle inequality and its variations really just how to apply it with limit proofs. I mean i understand it in terms of a triangle as no one side can be longer than the sum of the two other sides...
  37. Z

    Volume by cross-section: ellipse and equilateral triangle cross sections?

    Volume by cross-section: ellipse and equilateral triangle cross sections?? Homework Statement The base of a solid is the region bounded by the ellipse 4x^2+9y^2=36. Find the volume of the solid given that cross sections perpendicular to the x-axis are: a) equilateral triangles b) squares...
  38. K

    Need Help - Equilateral Triangle

    Homework Statement A particle moves from rest and has impressed a uniform velocity of 10 meters per second parallel to one side of an equilateral triangle, and a uniform acceleration of 10 meters/sec2 parallel to an adjacent side of the triangle. Find the distance of the particle from its...
  39. H

    Area of Triangle: How to Calculate

    Homework Statement Show that the area of a triangle with sides of lengths a and b with included angle theta is... A = 1/2 a*b*sin(theta) I am not sure what this question is really asking. Any help? Homework Equations The Attempt at a Solution
  40. A

    How Far Does a Particle Travel in an Equilateral Triangle with Mixed Motion?

    Homework Statement A particle moves from rest and has impressed a uniform velocity of 10 meters per second parallel to one side of an equilateral triangle, and a uniform acceleration of 10 meters/sec2 parallel to an adjacent side of the triangle. Find the distance of the particle from its...
  41. M

    Point charges and magnitude of the electric field at the center of a triangle

    Homework Statement A point charge q = 4.9 \mu C is placed at each corner of an equilateral triangle with sides 0.20 m in length. Is the magnitude of the electric field at the center of the triangle greater than, less than, or the same as the magnitude at the midpoint of a side? Explain...
  42. H

    Finding Velocity of Airplane & Wind: An Analysis of Triangle ABCD

    Homework Statement Airplane flies over route in shape of triangle ABCD. Time(t1, t2, t3) of flying over sections AB, BC, CA are known. Lenght of sections is also known. During fly wind is present. velocity of wind is constant, and speed of airplane relative to wind is also constant. Find...
  43. Somefantastik

    Proving Triangle Inequality for d(x,A) & d(y,A)

    Hey folks, can someone quickly check my algebra? Given: d(x,A) \leq d(x,y) + d(y,A) To show: \left|d(x,A) - d(y,A) \right| \leq d(x,y) Proof: from given, d(x,A) - d(yA) \leq d(x,y); and -d(x,A) + d(y,A) \geq -d(x,y); \Rightarrow d(y,A) - d(x,A) \geq -d(x,y)...
  44. E

    Total area of circles infinitely inscribed in isosceles triangle

    1. The base of the yellow triangle has length 8 inches; its height is 10 inches. Each of the circles is tangent to each edge and each other circle that it touches. There are infinitely many circles. The radius of the largest of them is __________ and the total area of all the circles is...
  45. N

    Net electric field with triangle

    Homework Statement A proton and an electron form two corners of an equilateral triangle of side length 5.3 x 10-6 m. What is the magnitude of the net electric field these particles produce at the third corner? Homework Equations E=kQ/r^2 The Attempt at a Solution I drew a triangle...
  46. T

    Area of a triangle by vectors - getting different answers

    Homework Statement A = (7,6,8) B = (2,3,-1) C = (2, -7, 9) Find the area of the triangle these 3 points make I'm getting slightly different results for different combinations I use if I take CA = a - c = (5 , 13 , -1) CB = b - c = (0, 10, -10) Taking another combination AB = b - a = (-5...
  47. C

    Area of triangle inside parallelogram

    Homework Statement http://folk.uio.no/robinbj/gg/ggstart.pdf" I am supposed to find the area of the triangle PQD. The numbers given are the areas of the other triangles.Homework Equations A= \frac{1}{2} a b \sin{C} As well as Heron's formula, possibly? A= \sqrt{s(s-a)(s-b)(s-c)} where s =...
  48. T

    Find the area of a triangle with vector sides

    Homework Statement Find the area of the triangle with vertices at the points with coordinates (1,2,3), (4,-3,2) and (8,1,1)Homework Equations The Attempt at a Solution well area of a triangle is 0.5 x base x height . We can get the length of each side by taking the modulus of each vector, but...
  49. J

    RMS of square, sine and triangle waves

    I'm trying to calculate the RMS for square, triangle and sine waves. I can easily do the integrtion for sine waves and for square waves by looking at the graphic and getting the areas. It doesn't seem as easy for triangle waves since its squared form looks much more complicated and I'm not...
  50. pellman

    What does the triangle equals sign mean?

    Looks like \triangleq. I first came across it on the wikipedia article for Lie derivative. http://en.wikipedia.org/wiki/Lie_derivative#The_Lie_derivative_of_a_function
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