What is Perimeter: Definition and 115 Discussions

A perimeter is either a path that encompasses/surrounds/outlines a shape (in two dimensions) or its length (one-dimensional). The perimeter of a circle or an ellipse is called its circumference.
Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter.

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  1. S

    Quadratic equations: Perimeter and Area fencing dimensions

    Homework Statement The following enclosure is built using 280 m of fencing. If the enclosure has a total area of 2800 m2, what are the dimensions to the nearest tenth? Homework Equations x = \frac{-b ± \sqrt{b^{2}-4ac}}{2a} The Attempt at a Solution Please note that the 3/2w and 5/2w...
  2. T

    Maximise perimeter of triangle in a circle

    Hey guys, I hope someone can give me some pointers with this because it should be really easy but I am just not getting it! I want to show that for a triangle inscribedin a circle an equilateral traingle gives the maximal perimeter. I've tried a few things and just get bogged down in algebra...
  3. P

    Finding the minimum perimeter.

    Homework Statement I'm stuck on part b) of the question, but this includes the whole thing: A farmer wants to make a rectangular paddock with an area of 4000m^2. However, fencing costs are high and she wants the paddock to have a minimum perimeter. a) Show that the perimeter is given...
  4. S

    Perimeter and surface area of skewed end semi cylinder

    I want to calculate the surface area of semi cylinder with one or both ends skew at a given angle. To calculate the area/perimeter i need to find out the end profile of the semi cylinder. If the skew plane is perpendicular to the cylinder axis, the cut surface would be half ellipse with major...
  5. D

    Finding the sides of a trapedzoid using only Angles and perimeter

    Homework Statement My knowns are: the trapezoid has a perimeter equal to 180 inches and it's base angles are ∏/3 The unknowns are: the lengths of the base (x) and the length of one of the slanted sides (y) as well as the relationship between x and y Homework Equations Trig equations...
  6. veronica1999

    MHB What is a simpler method to find the perimeter of triangle AMN?

    Triangle ABC has side-lengths AB=12,BC=24,and AC=18. The line through the incenter of ABC parallel to BC intersects AB at M and AC at N. What is the perimeter of triangle AMN? (A)27 (B)30 (C)33 (D)36 (E)42 My friend is saying my solution is too messy and there was no need for the heron's...
  7. J

    Geometry question with the perimeter of a circle

    say I have a circle with a diameter of d and there is a point at the top of the circle, p. I want to know the distance from point p to any other point on the perimeter and the angle θ from the tangent line of p. is there a function that will describe this? I will try to put up a picture to...
  8. D

    Comp Sci Finding the perimeter of evolving objects in Fortran

    Hello fellows, I am writing a computer program in Fortran, to find the perimeter of multiple squares. These squares move as "time" goes along, and if they come in contact with each other, they stick together, forming clusters. The reason why I'm doing this in Fortran is because the original...
  9. F

    Proof: circumference of circle inscribed in a triangle < perimeter of the triangle

    Homework Statement A circle is inscribed in a triangleHere is a picture Picture of circle inscribed in triangle, not necessarily to scaleWhich is larger: the circumference of the circle, or the perimeter of the triangle? Homework EquationsC=∏D (D=diameter of the circle, C=circumference of...
  10. veronica1999

    MHB Help Me Find the Perimeter of Tn+1

    Could I get some help please?Let T1 be a triangle with sides 2011, 2012, and 2013. For n > = 1, if Tn = triangle ABC and D, E, and F are the points of tangency of the incircle of triangle ABC to the sides AB, BC, and AC, respectively, then Tn+1 is a triangle with side lengths AD, BE, and CF, if...
  11. marcus

    Rovelli's talk at Perimeter 4/4/12: video online, comment?

    http://pirsa.org/12040059 Fine presentation today, room packed, good questions from audience (esp. from Turok but also from others.) Rovelli will spend several weeks at Perimeter during which time he also makes a side trip to Princeton Institute for Advanced Study to give a slightly different...
  12. L

    Setting area = perimeter of rectangle, does it have any meaning?

    Suppose I have a rectangle with length x and height y:Can this ever be true? That xy = 2x+2y? My guess would be that area of a shape can never equal the perimeter of that shape. And that would be confirmed by the fact that the equation is always false (except if both variables equal zero...
  13. GreenGoblin

    MHB Max Area of isosceles triangle with perimeter 1

    Given this seemingly simple problem of maximising the area of an isosceles triangle with perimeter equal to 1. What is the best approach and how will I find a result easiest (I know how to get the answer but I need to be able to do these problems fast, so please help me look for a quick method...
  14. N

    Acceptance/rejection dates for Perimeter Scholars Institute (Canada)?

    I was wondering if anybody knew about when I should hear back from PSI? I realize the chance someone will be able to give me an answer is small, as it is not stated on their site and the course is only about 3 years old so few people have experience with it, but I was thinking that it's not...
  15. C

    Graduate programs like Perimeter Institute for math?

    Hello all, I was wondering if anyone knew if there are programs like Perimeter Scholars International for mathematics (rather than largely physics)?
  16. P

    Perimeter and area - need explanation

    Dimensions of rectangle are a=2 and b=5. Perimeter and area P=2a+2b=14 and A=a*b=10 If we take a rope of length l=14m, encircle the rectangle and connect the ends we will have the same perimeter. Now we take this rope and make circle of it, this circle will have the same perimeter of...
  17. M

    Propagation error in finding the perimeter and area, .

    Homework Statement I want to measure the size of my back yard. I estimate that I can measure the length and width of the yard using a tape measure to an accuracy of 0.05m. I find that the length of the yard is 8.6 m and the width is 7 m. Calculate the perimeter of the yard and its...
  18. I

    Express the length of the hypothenuse as a function of the perimeter.

    Homework Statement The altitude perpendicular to the hypothenuse of a right triagle is 12 cm. Express the length of the hypothenuse as a function of the perimeter. I found a very elegant solution for the problem and even mathematia agrees on that asuming the equations i start with are right...
  19. D

    Optimization problem involving an area and perimeter

    My friend and I have come across this problem in Apostol's Calculus Vol. 1, ed.2 (exercises 4.21 if anyone is looking). We are studying calculus independently and have become stumped by this one. Homework Statement The problem as written in Apostol: "A farmer wishes to enclose a rectangular...
  20. Femme_physics

    Calculating Perimeter: Circle Sidewalk with a Radius of 220m and Width of 30m

    Homework Statement http://img94.imageshack.us/img94/9216/thethingy.jpg Through a circle roundabout whose radius is 220 meters, they constructed a sidewalk in width of 30 meters. Calculate the perimeter of the sidewalk. The Attempt at a Solution perimeter of a circle equation: 2 x...
  21. menniandscience

    How to measure perimeter without pi?

    how to measure perimeter without pi? [before they knew about the pi ratio]
  22. D

    Question about perimeter weighting in golf clubs

    From How Stuff Works: "In the last 25 years, designers have developed clubs that have approximately the same weight as the older clubs but have it distributed around the perimeter of the club, so that the head is far more resistant to off-center twisting and therefore far more forgiving of...
  23. marcus

    Spin Foams and Noncommutative Geometry (video, Marcolli at Perimeter)

    Marcolli has been a frequent collaborator with Alain Connes, and is now math prof at Caltech. Since NC geometry has yielded the Standard Model particles, plus some predictions, there is interest in basing the NC matter on spinfoam quantum geometry http://pirsa.org/11020110/ Spin Foams and...
  24. G

    Programs Cambridge Part III vs Perimeter Institute master program

    Hello! Suppose that your objective is to do a PhD in an american university, one of the top to be exactly. Imagine you have to opportunity to chose between Cambridge Part III and Perimeter Institute master program. Which master would be the best way to achieve the stated goal? What would be the...
  25. U

    Maximising the area of a triangle of known perimeter

    How would I find the maximum area of a triangle given a fixed perimeter? I assume that it would be an equilateral triangle, but I'm finding it very hard proving it. I started by drawing a triangle of side lengths a, b and P -(a+b) with angles of alpha, beta and gamma. I then used the...
  26. P

    Perimeter & Area: Which Structure Has Largest/Smallest?

    I had a question on a test & could not get an answer and was wondering if someone might have a clue. The question presented four buildings--a square, rectangle, L-shaped building and circle. All of the buildings are one-story and have the same area. The question was which structure had the...
  27. I

    Internship at the Perimeter Institute

    Hi, I am currently studying fundamental physics at University Paris 6 as an undergraduate (accomplishing my 4th year). I have to make an intership for 3months next summer, and I would like to it in theoretical physics (already did one in an experimental lab and i would like to see the other...
  28. K

    Quadratic Question Dealing With Perimeter

    Homework Statement Jillian is getting ready to send a holiday package in the mail. The rectangular package has a square base and the sum of all the edges of the package measures 140 cm. What dimensions will produce a package with the largest possible surface area? Homework Equations...
  29. C

    Movement of a point on the perimeter of a disc

    Homework Statement a disc of radius r spins uniformly around its axis at an angular velocity \omega in a clockwise motion. the center moves on the horizontal line z = r of a vertical axis Oxz of the referential Oxyz. We call R' = Cxyz, in translation compared to R= Oxyz, of origin C and we...
  30. S

    Calculating the Perimeter and Area of a Square MIKE

    [b]1. given a square MIKE, point U, U is an interior point, L is the midpoint of IK, then MU is a segment equal to segments EU and LU which is equal to 10 units. What is the perimeter of MIKE and the Area of IULK? [b]2. P= 4s, A=1/2h(b1+b2) [b]3. P=4(20), P=80 A=1/2(10)(10+20)...
  31. N

    From Europe to Perimeter Institute

    Hello, I've read through ZapperZ's "walkthrough" until the PhD-section to get some info and it did help. More specifically: I'm doing my undergraduate studies in Belgium and I was wondering what it takes to apply to PI. This might seem like a silly question, but the system is really quite...
  32. K

    Perimeter Scholars Lecture Archive

    I'm not necessarily sure if anyone has posted this archive of Perimeter Scholars International Lectures but I suppose that if it has or hasn't they'll serve as a distinctive and quantitative approach to understanding rigorous and advanced physics topics. The link is the following...
  33. O

    Courses Courses in Quantum Computing at Waterloo, IQC & Perimeter

    Hey , I want to know about the courses in quantum computing at univ. of waterloo or IQC or perimiter institure for international students and also the procedure and other formalities to apply there??I have done masters in physics and currently having a 2 year IT exp. under my belt. i want...
  34. rhody

    Hawking to leave Cambridge in protest over budget cuts, heading to Perimeter

    Score one for Perimeter, it would be great if Hawking Radiation is confirmed so he could receive a Nobel and be recognized before his health fails him. http://www.dailymail.co.uk/news/article-1254945/Stephen-Hawking-plans-leave-Britain-Government-cuts-science.html"
  35. marcus

    Livine's Feb 17 talk, if you only watch one Perimeter talk this year

    http://pirsa.org/10020079/ Great talk about cool results. Perimeter has videos of a lot of excellent valuable lectures on line but if you would only watch one, be sure it's this :biggrin:
  36. marcus

    QG with an Orsay accent (what I got from the Perimeter AsymSafe conference)

    For me the most exciting talk, with the most new content, was by Vincent Rivasseau. He is at Orsay. That means the top Paris center for physics theory. We should get some slight acquaintance with the person, as well as his current research. http://www.rivasseau.com/index.html Born in 1955...
  37. H

    Minimising the perimeter of a tunnel with a fixed area

    Homework Statement A tunnel cross-section is to have the shape of a rectangle surmounted by a semicircular roof. The total cross-sectional area must be A, but the perimeter minimised to save building costs. Find its dimensions Homework Equations The Attempt at a Solution I have...
  38. R

    Perimeter of an elipse - exact formula

    perimeter of an elipse -- exact formula I found an exact formula for the perimeter of an ellipse in terms of its major and minor axis a = 1/2(major axis) b=1/2(minor axis) my equation for the perimeter of an ellipse...
  39. R

    What is the exact formula for finding the perimeter of an ellipse?

    perimeter of an ellipse -- exact formula I found an exact formula for the perimeter of an ellipse in terms of its major and minor axis a = 1/2(major axis) b=1/2(minor axis) my equation for the perimeter of an ellipse...
  40. marcus

    Perimeter gets Loll to teach 3-week QG minicourse

    http://www.perimeterscholars.org/course-curriculum.html Perimeter Scholars International is an interesting 10 month educational concept where you earn a Masters degree in theoretical physics (cosmology, quantum gravity, condensed matter, string, foundations, quantum information---broad range...
  41. J

    Maximizing the Area of a Pentagon with Fixed Perimeter

    Homework Statement a pentagon is formed by placing an isosceles triangle on a rectangle. If the pentagon has a fixed perimeter P, determine the lengths of the sides of the pentagon that maximize the area of the pentagon Homework Equations The Attempt at a Solution not sure...
  42. L

    Solving for perimeter and dimensions of a rectangle

    I understand calculus, I just don't understand how it is applied to solve these sorts of problems. Homework Statement What is the smallest perimeter for a rectangle with an area of 16, and what are its dimensions?Homework Equations A=L*W P=2W+2L The Attempt at a Solution I managed to get the...
  43. P

    Perimeter of a triangle which circumscribes by 3 circles

    Hello, I need help with this problem please (this is counted as large part of my grade so please hel) thank you Problem: Each of three congruent circles has radius 1, and each is externally tangent to the other two. An equilateral triangle circumsribes this configuration, so that each...
  44. U

    Finding the trapezoid of smallest perimeter given a,b,h

    Hi all, It seems obvious that the trapezoid with the smallest perimeter given the lengths of the bases and the height is the isosceles trapezoid. How can I prove this (preferably using analytical methods)? Note: this is not homework or anything. I need to know this as a step to prove the...
  45. J

    General Relationship Between Area & Perimeter

    This is kind of a vague question but does anybody know if there is a more general relationship between the area and perimeter of plane figures. For example circles, squares, rectangles triangles any regular polygon really, the area can be written in terms of the perimeter. Is there anything...
  46. L

    Why is the area of an ellipse simpler than its perimeter?

    Why does the area of an ellipse have a closed form while the perimeter does not? Obviously if the area is finite so is the boundary so it seems the perimeter should be calculable in a closed form.
  47. marcus

    Physics law evo video (from the Perimeter quantum time conference)

    http://www.perimeterinstitute.ca/Events/The_Clock_and_the_Quantum/Abstracts/ The week ending 2 October there was a conference on time and quantum theory at Perimeter. Some who gave talks were Lee Smolin Roger Penrose Neil Turok Leonard Susskind William Unruh Rafael Sorkin ... The link gives...
  48. L

    Why does adding 1 meter to a rope around the Earth create slack?

    First, try to use your own sense. Take a twine (rope) and put it around a ball, or an orange (sphere). Now you have the circumference (perimeter) of that sphere. Take this twine and add 1m more (one more meter - it can be any unit of liner measure). Put this one meter longer twine around...
  49. M

    Max Area of Rectangle Yard Using X Fence Feet: Math GRE Q13

    Question: A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum possible area of the yard, in terms of x? Answer: My first guess is x^2 / 9 if you assume the yard is square. I'm a little unsure of my answer since for either the horizontal...
  50. P

    Proving Circle Has Smallest Perimeter for Same Area

    Hi everybody, In physics and mathematics, we often use the theorem that the circle alway has the smallest perimeter compared to all other geometric shapes of the same area. Anyone can tell me how to prove that? Thanks for reading.
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