Triangles Definition and 211 Threads

Hi Given is a triangle on points x,y,z in the plane. This triangle has two points a and b on opposite sides (see Figure). I would like to show that the following inequality has to hold: \max {d(b,x), d(b,y), d(b,z)} + \max {d(a,x), d(a,y), d(a,z)} - d(b,a) > \min {d(x,y), d(x,z)...

Hello, I am working on a project that involves using 2D triangles to build 3D models and I am looking for software that will allow me to draw 2D triangles based on the triangles 3 edge lengths (ex: 4 cm x 5 cm x 3 cm). Most of the software I have found requires knowing either the triangles...

Homework Statement Show that the angles a, b, c of each triangle satisfy this inequality. \tan \frac{a}{2}\tan \frac{b}{2} \tan \frac{c}{2} (\tan \frac{a}{2} + \tan \frac{b}{2} + \tan \frac{c}{2}) < \frac{1}{2} Homework Equations The Attempt at a Solution I used the half angle...

Homework Statement Ok, I have this problem this week. (1) Consider\ a\ tiling\ of\ the\ unit\ sphere\ in\ \mathbb{R}^{3}\ by\ N\ equilateral\\ triangles\ so\ that\ the\ triangles\ meet\ full\ edge\ to\ full\ edge\ (and\ vertex\ to\ vertex).\\ Show\ that\ the\ only\ possibilities\ for\ N\...

Hi, I did a search in the forums and found a similar problem, but nothing on this particular one. I have a problem asking for a procedure to find the number of toothpicks in any figure in a sequence, with an illustration that shows the first three figures of the sequence of triangles built with...

Hi everybody; I am a bit stuck with negative angles. What I know is that: If we measure an angle from x-axis clockwise direction, the angle is negative. However, I am a bit dissapointed because while I researched the web I see the negative agles only in topics subject to trigonometry. So I...

1. How does the moon's diameter compare with the distance between Earth and the Moon Tape a small coin, such as a dime to a window and view it with one eye so that it just blocks out the full Moon. This occurs when your eye is about 110 coin diameters away. Then the ratio of coin diameter/...

Why do we study so much about right triangles like trigonometry. We could define sin and cos like functions in a 70 degree triangle too. I also know right triangle is something special but i don't know what is it. Also why won't trigonometry on other type of triangles be not so good

A Right-Angled Triangle has area Acm^2 and perimeter Pcm. A side other than the hypotenuse has length has length xcm. Form a quadratic equation in x in each of the following cases: a) a=6 p=12 let the other side be y, and the hypotenuse be h x + y + h = 12 0.5*y*x = 6, y= 12/x x + 12/x...

I'm trying to figure out how to integrate a data set, without knowing the function. While doing this, I got to thinking about this: If the definite integral of a function can be represented by the area under that function, bound by the x axis, then shouldn't: \int_{a}^{b}2x\frac{\mathrm{d}...

when a cable car is stationary,it is in equilibrium.So the forces acting on it forms a closed triangle.(the vector diagram) Why is the triangle an isosceles triangle? I did this question on my paper and stumbled across this on the answers,couldnt figure out why hope someone could enlighten me!

I have two triangles in 3d. I need to calculate transformation matrix(3X3) between two triangles in 3D. 1)How can I calculate the transformation matrix(rigid) while fixing one of the points to the origin(to get rid of the translation part)? 2)How does it affect if the deformation is non rigid?

errrr, THEOREM >.< ... oops ... Homework Statement Prove that when edges of a complete heptagon are colored with two different colors, there will be at least three pure triangles.Homework Equations The Attempt at a Solution i can do two pure triangles, but not three :cry: pick a vertex v. It...

I learned trignometry on the basis of right-angled triangles.Is it applicable to all(acute and obtuse) triangles?and how do you explian cos or sin(<=90),since it's no longer associated with right angled triangle?.can anyone please clarify.

Hello everyone, This is my first post on here, I was hoping it wouldn't be asking for help but I don't have any options left and it's a problem that is due soon. I promise I have tried to solve it myself but I'm unsure if I'm doing it correctly and it is part of a take home test. Homework...

Homework Statement Okay. I thought I knew how to do these type of questions, but here goes. The node at a is attached to the positive terminal of a voltage source and c is attached to the negative. I'm completely bemused as to how to reduce this circuit into a single-resistor equivalent...

Side note: PF is awesome! This is kind of like Tutor.com, only it's free and others can contribute their answers. Homework Statement Explain why triangle ABD is similar to triangle ABC and then find the length of side AB. Angles B and C are congruent. m(ADB)+m(BDC) = 180 degrees. AD=4 and...

What is ceter of gravity concept and how to calculate it for a triangle

Hi I am a noob on here, first post. Not a physicist by any stretch, but am researching the quantum mind and a while ago came across a paper that proposed that the quantum foam (if that is the correct term, maybe spacetime?) was geometrically just a bunch of triangles. If anyone can post a link...

Homework Statement So these are line segments in triangles. I don't understand how they are different. Homework Equations The Attempt at a Solution

http://www.ufoevidence.org/Cases/CaseView.asp?section=Triangle http://www.ufoevidence.org/topics/triangles.htm They have been sighted all over the world including a friend of mine who saw it up close just hovering about 4 storey high in a 2 storey home almost covering it. Who created them...

This thread is concerned with rectangular triangle with one side ( = s) and hypothenuse (t = 2 s + 1) given and we are looking for the remaining side (all sides having integer values) d^{2} = t^{2} - s^{2} = (2 s + 1)^{2} - s^{2}, with d, s, t \in \mathbb{Z} Computational experiments...

Homework Statement http://i54.tinypic.com/2cdib6t.jpg Since its trig, here is a scan. Homework Equations The Attempt at a Solution I thought it was similar triangles, so i used ratio to solve it as 10.4. what if it asks for me ar angle instead of a side? is that...

Homework Statement If a polygon has n>=4 sides, what is the probability, in terms of n, that a triangle made up of vertices of the polygon shares at least one side with the polygon. Homework Equations The Attempt at a Solution Treating vertices of polygons as possible outcomes...

My girlfriend is re-learning geometry. She has noticed that the sum of the angles of a triangle is equal to the measure of a straight angle and half the measure of a full revolution. She wants me to ask if there is any special relationship between a triangle and a straight angle or between a...

Homework Statement ABCD is a parallelogram. E, F are points on the straight line parallel to AB. AF, BF meet at P, and DE, CF meet at Q. Prove that PQ ll AD. 2. The attempt at a solution I drew the diagram. I tried to solve the problem in this way:- CD ll XY Therefore, [SIZE="3"]angleCDE =...

X = ?

CONJECTURE: Subtract the Absolute Values of the Stirling Triangle (of the first kind) from those of the Eulerian Triangle. When row number is equal to one less than a prime number, then all entries in that row are divisible by that prime number. Take for instance, row 6 (see below). The...

Can the cosine law be used on right triangles as well as oblique triangles?

Homework Statement A man 6 feet tall walks at a rate of 5 feet per second away from a light that is attached to a pole 15 feet above the ground. At what rate is the length of his shadow changing when he is 30 feet from the base of the pole? I get that this is really like a two similar...

Homework Statement ABC and BDE are two equilateral triangles such that D is the midpoint of BC. If AE intersects BC at F, show that :- (i) ar(BDE) = 1/4 ar(ABC) (ii) ar(BDE) = 1/2 ar(BAE) (iii) ar(ABC) = 2ar(BEC) (iv) ar(BFE) = ar(AFD) (v) ar(BFE) = 2ar(FED) (vi) ar(FED) = 1/2ar(AFC)...

Homework Statement Please see the attached figure The radius of the biggest circle is 10. The required is the sum of all circles and the sum of all triangles in the figure. There is an infinite number of circles and triangles. My answers are: for circle: 475/3 pi for triangle: 175/2...

Homework Statement This may be basic, but how do you know which part of an integration problem fill the up the triangle values for trig substitution?

I am reading about "special triangles" 45.45.right angle. I was reading how they found the ratios of the sides of a triangle. It looks like they let the leg opposite of the 45 deg angle be length A and the corresponding 45 deg angle be length A aswell.. then they used the Pythagorean theorem...

Lately this has been bothering me, I hope you can understand the point I'm trying to make. On a side note, this topic maybe more philosophical than mathematical. It comes down to this. In a right triangle, why is the length of the hypotenuse not equal to the length of the adjacent side plus the...

Limiting ourselves to N... Conjecture: (sqrt (16x + 9) - 1)/2 = y | 2y^2 + 2y - 3 = z^2 for x = a Sophie Germain Triangular Number, which is recursively defined as: a(n)=34a(n-2)-a(n-4)+11 First 11 values (I have not checked further as I would be very surprised if this equivalency...

Homework Statement The diagram below shows four congruent circles whose centres are the vertices of the square DEFG and whose circumference touch the sides of an isosceles triangle. Area of triangle ABC is 10000 units square. What is the radius of the circles, to the nearest unit...

I have always heard that triangles are the strongest geometric shapes. Can anyone explain why this is so?

Homework Statement In the following diagram D and E are the midpoints of AB and AC. Use vector methods to prove that DE = 1/2BC Homework Equations DE = 1/2 BC The Attempt at a Solution AD = 1/2AB AE = 1/2AC AD + DE = AE DE = -AE + AD DE = -1/2AC + 1/2AD IF BC = -AC + AB AND DE = -1/2AC +...

[b]1. Prove that a graph with n vertices that has no triangles has at most (n^2)/4 edges. [b]2. [b]3. Um so i was thinking maybe you start off with a complete graph and then keep deleting edges so as to remove the triangles within it or something? Or maybe by induction?

Prove that there exist (a) 5 points in the plane so that among all the triangles with vertices among these points there are 8 right-angled ones; (b) 64 points in the plane so that among all the triangles with vertices among these points there are at least 2005 right-angled ones.

http://a.imageshack.us/img715/8526/paint2.jpg there are 2 triangles. in these triangles r1,a,theta1 r2,a,theta2 are given. x1 and x2 are unknown. also the angle k is same for both triangles. i need to find this k. also i have data to draw series of tingles like these 2(i know r3,theta3,a...

2 isosceles triangles ABC and ABD have the same base AB but are in different planes. Prove that CD is perpendicular to AB. (It must be proved that CD is perpendicular to one of the planes and then it is perpendicular with every segment of this plane.) Thanks in advance!

Homework Statement For each positive integer n, let T(n) be the number of triangles with integer side lengths, positive area, and perimeter n. For example, T(6) = 1 since the only such triangle with a perimeter of 6 has side lengths 2, 2 and 2. (a) Determine the values of T(10), T(11) and...

Homework Statement Is any formulas similar to that of proportionality of the triangles to proportionality of the given figure? Homework Equations The Attempt at a Solution

As someone who has just started Physics, when triangles were introduced in my physics it caught me in surprise. If the legs of triangle were heights It would somewhat make more sense to me, but our teacher says their are velocities. I do not understand. For example : A pitched ball is...

I've notice that our eye balls are spheres, our Earth is a sphere and our sun is a sphere.. Now that makes me wonder. If our universe is a sphere, i already know scientist think so, but its still something to even think more into. Now this is the big part, triangles are important as well. Like a...

Homework Statement How come all thetas are equivalent? Please take a look at this drawing http://tinypic.com/view.php?pic=2aahe3d&s=4 The Attempt at a Solution By similar triangles?

Homework Statement A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole? Homework Equations...

Here's the question: The leaning Tower of Pisa leans toward the south at an angle of 5.5°. On one day, its shadow was 90m long, and the angle of elevation from the tip of the shadow to the top of the tower is 32°. Determine the slant height of the tower. How high is the tip of the tower...