Plane geometry Definition and 18 Threads

It's very easy to prove the area formula for a rectangle when both length and width are positive integers, but I cannot prove it when length or width or both are rational or irrational numbers. I need an intuitive proof that is as simple as possible without using very advanced math like calculus.

This is a common exercise stemming from special theory of relativity courses all over the world it seems. Show that the intersection of scissor blades can move faster than the light. If we imagine that we put a pen in between the scissors, touching the blades, and it is sliding without much...

Currently, as far as I know, the two main ways to express any given point on a plane is through either cartesian plane or polar coordinates. Both of which requires an ordered pair of two numbers to express a point. However, I wonder if there exists such a system that could express any given...

I don't get what is meant with the last part: that takes any one given point to any other given point. Thanks in advance

Before looking at the proof of basic theorems in Euclidean plane geometry, I feel that I should draw pictures or use other physical objects to have some idea why the theorem must be true. After all, I should not just plainly play the "game of logic". And, it is from such observations in real...

Homework Statement Describe and sketch the geometric objects represented by the systems of equations Homework Equations x2 + y2 + z2 = 4 x + y + z = 1 The Attempt at a Solution I can sketch both objects: 1) sphere with center (0,0,0) and radius 2 2) "simple" plane with intersection...

Mod note: Moved from a technical forum section, so missing the homework template. @fab13 -- please post homework problems in the appropriate section under Homework & Coursework. I have the following exercise to solve : I have to find all the points on the surface ##x^2+y^2+z^2=36## (so a sphere...

Hello, I am totally bad at geometry , by geometry I mean plane euclidean geometry with similarities and circles. I sometimes feel totally lost with problems. For example: The parallel sides of trapezoid ABCD are 3 cm and 9 cm(AB and DC).The non parallel sides are 4 cm and 6 cm(AD and BC).A...

Homework Statement Problem 99 from "Kiselev's Geometry Book I - Planimetry": Two isosceles triangles with a common vertex and congruent lateral sides cannot fit one inside the other. Homework EquationsThe Attempt at a Solution The statement is obviously true. If we visualize each isosceles...

Homework Statement Problem 55 from Kiselevś Geometry - Book I. Planimetry: "Prove that each diagonal of a quadrilateral either lies entirely in its interior, or entirely in its exterior. Give an example of a pentagon for which this is false." Homework EquationsThe Attempt at a Solution The...

What is the difference between the Euclidean Geometry and the simple plane geometry? They seems to work with flat planes.

Hello, After reading both How to Prove It: A Structured Approach - By Daniel J Velleman, and one of the Lost Feynman Lectures on Planetary Orbits, I'm wondering if anyone could suggest to me any good books they've read (or heard about) pertaining to logic (paired with analysis), or plane...

Homework Statement Find the equation of plane which contains the line l:\left\{\begin{array}{l} x=t+2 \\y=2t-1\\z=3t+3 \end{array}\right., and makes the angle of \frac{2\pi}{3} with the plane \pi:x+3y-z+8=0. The Attempt at a Solution My attempt was to find the normal vector of plane which...

Consider a point P inside a triangle ABC. Angle PBC is 10 degrees, angle PCB is 20 degrees, and angle BAC is 100 degrees. Find angle PAC. Question is that is this problem even solvable? I found it in an Olympiad training book...

Hi everyone, Can anyone solve the followong by plane Euclidean geometry? I got it by co-ordinate geometry, but couldn't get it by plane... >In an acute - angled triangle PQR , angle P=\pi/6 , H is the orthocentre, and M is the midpoint of QR . On the line HM , take a point T such that...

Hey there I do study a textbook at School called Plane Geometry, it is about 3d dimensional figures, it starts with explaining Planes, points and lines, then It starts with theories, then I have to prove something like a line perpendicular to a plane and things like that. I googled Plane...

This is the last problem on a geometry problem set that I can't seem to finish. AB and BC are chords in a circle where AB > BC. D is the midpoint of minor arc ADBC. If DE is perpendicular to AB, prove that AE = EB + BC. I would really appreciate just the proper way to approach this...

PQR is an equilateral triangle, and A is a point on QR such that RA = 2 QA. Prove that PA^2 = 7QA^2 If someone can help, i'd really appreciate it. Thanks