So if the moment of inertia of the rectangle is, about its centroid, is bh cubed over 12, and the moment of inertia of the hole, the circle, from the previous tables is pi r to the 4th, over 4. This tool calculates the moment of inertia I of a triangle (triangular lamina). Please use consistent units for all input. to x-axis is c p c c I h h h A where 3 36 c W L I is the area moment of inertia for a triangle with respect to the (depth of the) centroid c h. Q The moment of inertia of an area about an axis is equal to the area moment of inertia about a. Standard Beams Common Beams Applications Beam Bending Geometric Shapes Common Shapes Circle Circular Section Triangle Parabola Regular Polygon Rectangle Common Solids. 4ft4 and Iu0. This is a suppliment to the tutorial, and is here only for illustrative purposes Gibbous moons also wax and wane depending on its time in the cycle They will also need to be able to look for lines of. Hint Assume that mass of an equilateral triangle is concentrated about its vertices and first determine the moment of inertia of the entire lamina by finding the distance between the lamina&x27;s centre and its vertices. From Triangles to Polygons. - The distance &x27;r&x27; from any vertex of the. T h y. Suppose PQR is a triangle having a centroid V. Moment of Inertia of Isosceles Triangle Formula Mathematically,. In the same manner, the transfer formula for polar moment of inertia and the radii of gyration are respectively. Centroids and Moment of Inertia Calculation. You can not only determine this particular quantity, but also area, centroid of beam, and section modulus by using this free calculator. The convention is to place a bar over the symbol I when the the axis is centroidal. It mainly depends on the distribution of mass around an axis of rotation. An area with an axis of symmetry will find its first moment of area with respect to that axis is equal to zero i. Question 9. Centroid, Area, Moments of Inertia, Polar Moments of Inertia, & Radius of Gyration of a Isosceles Trapezoid. For point P, we have. Find the centroid of the region bounded by the cubic curve the vertical line x 1,. The moments of inertia of the plane region about the x- and u-axes are Ix0. The current page is about the mass moment of inertia. MECHANICAL ENGINEERING 12 MOMENT OF INERTIA AREA Mechanical Engineering Ch 12 Moment of Inertia (41 of 97) 2nd Moment of Area Triangle 13 30,798 views May 2, 2017 258 Dislike. The moment of inertia of a triangle with respect to an axis passing through its base, is given by the following expression I fracm h26 This can be proved by application of the Parallel. 1 Describe the geometry and operation of a human peristaltic PDP which is cherished by every romantic person on earth. 2K Visits in Oktober 2022 und das. Axis passing through the centroid. 67) 4. 2 Ara 2022. Example 10. y 2 b h 0 h b h y 2 d y Simplifying, y 2 h 2 y 3 3 0 h y 2 h 2 h 3 3 0 y 2 3 h. Search Shapes With Curved Sides. Iz, A, Yc minertia(ASpec) returns the moment of inertia Iz, the total area A, and the centroid Yc of the area. Skyciv moment of inertia renault truck bluetooth not working Fiction Writing Gem&228;&223; den Daten zu den monatlichen Visits von Similarweb hei&223;t der gr&246;&223;te Wettbewerber von clearcalcs. leaked debit cards with money 2020. 2-To get the moment of inertia at the Cg of the isosceles, which is termed Ix CG at the CG of the isosceles. Base Angle of Isosceles Triangle. 3b) Where dA is the area of an element x, y stands for distance of the element from y and x axes respectively. The role of the moment of inertia is the same as the role of mass in linear motion. To observe the derivation of the formulas below,. In geometry, an isosceles triangle (assliz) is a triangle that has at least two sides of equal length. In other words, area of a rhombus is half the product of its diagonals. Moment of inertia of an area is expressed as fourth power of the distance, that is cm4, mm4 or m4. Moment Of Inertia Formulas Pdf. 559) 38894(0. Moment of Inertia is defined as I m r 2. The second moment of area, also known as area moment of inertia, is a geometrical property . The moment of inertia relative to centroidal axis x-x, can be found by application of the Parallel Axes Theorem (see below). The moments of inertia of the plane region about the x- and u-axes are Ix0. Expert Answer Who are the experts Experts are tested by Chegg as specialists in. For the rectangular region, determine (a) the principal moments of inertia and the principal directions at the centroid C; and (b) the moments and products of inertia about the u-v axes. Let ABC be a right-angled isosceles triangle where AB BC a. Calculate the moment of inertia of an equilateral triangle made by three rods each of mass m and length l, about its centroid. leaked debit cards with money 2020. Let ABC be a right-angled isosceles triangle where AB BC a. In isosceles triangle RST, angle S is the vertex angle. Be aware that we need to use the parallel axis theorem for the 3 triangles which enclose the central triangle. Our People - Texas A&M University School of Architecture. Now, area of triangle ABD 12. Polar Moment of Inertia about the z 1 axis J z1. - Moment of inertia along I xx (64) D 4 - Moment of inertia along I yy (64) D 4 - For semi-circle I xx 0. It mainly depends on the distribution of mass around an axis of rotation. 14 C. 1 An engineer claims that flow of SAE 30W oil, at 20C, through a 5-cm-diameter smooth pipe at 1 million Nh, is laminar. Hint break into two right triangles and use parallel axis theorem. The first moment of area of the entire polygon about its own centroid is always zero. We compute the center of pressure for both bottom and inverted isosceles triangle using the integral and the formula with the area moment of inertia Ic and find that for both triangles. Relevant Equations moment of inertia. C Distance to Centroid, in or mm; I Second moment of area, in 4 or mm 4; J i Polar Moment of Inertia, in 4 or mm 4; K Radius of Gyration, in or mm; P Perimeter of shape, in or mm; Z Elastic Section Modulus, in 3 or mm 3; Online Circle Sector Property Calculator. The moment of inertia of a triangular section of base B and height H about an Axis passing. Calculate the moment of inertia of an equilateral triangle made by three rods each of mass m and length l, about its centroid. The surface area of a pyramid is equal to the sum of the areas of each side of the pyramid. Search Shapes With Curved Sides. . Solve for the moment of inertia of the complex figure by subtracting the moment of inertia of area 2 (A2) from area 1 (A1). I MOI of A1 - MOI of A2 I bh 3 12 - bh 3 12 I (50. Moment of Inertia of Isosceles Triangle Formula Mathematically, About The Author Jalal. Figure 17. Ix 1 12bh3 Iy 1 12b3h. The SI unit of moment of inertia is kg m 2. For the Isosceles triangle shown to the right, find the moments of inertia, Ix and Iy, about the centroidal axes. 17, 2016 8 likes 11,743 views Download Now Download to read offline Education fast trics to find centroid and moment of inertia sachin chaurasia Follow Advertisement Recommended Chapter 4 krishndesai 1 centroids ELIMENG Properties of surfaces-Centre of gravity and Moment of Inertia JISHNU V Centre of Gravity. Moment of Inertia of Isosceles Triangle Formula Mathematically, About The Author Jalal. elvui name text format. 0) 1500(0. de 2021. de 2013. The Passage of an Axis via the Centroid The picture is showing a triangle and a line that is passing through the centroid. Here is the application of the parallel axis theorem to calculate ly&x27;. Moment of Inertia of Isosceles Triangle Formula Mathematically, About The Author Jalal. h 2 dA. But the moment of inertia of the big triangle can be also split into 4 moments of inertia. 6ft4, respectively. - The distance &x27;r&x27; from any vertex of the. S, T and U are the midpoints of the sides of the triangle PQ, QR and PR, respectively. 1 Centroid and First Moment of Area 11. Mass Moment of Inertia of a Triangle · 1. For each axis (x-x and y-y) exists one moments of inertia (Ixx and Iyy) and as the distance to the outer fibre is different in angle position (a) and (b) there are two section modulus for each. Calculate the moment of inertia of an equilateral triangle made by three rods each of mass m and length l, about its centroid. 2 hours ago by. An isosceles triangle has its centroid located somewhere on the line of symmetry that . The moment of inertia, or more accurately, the second moment of area, is defined as the integral over the area of a 2D shape, of the squared distance from an axis where A is the area of the shape and y the distance of any point inside area A from a given axis of rotation. CENTROIDS AND MOMENTS OF AREAS 11. Its moment of inertia about the axis passing through the centroid and prependicular to the plane of the lamina is - <br> <img src"https . In this case the plane of the figure always remains perpendicular to Hp. The formula for the centroid of the triangle is as shown C e n t r o i d C (x, y) (x 1 x 2 x 3) 3, (y 1 y 2 y 3) 3. The calculated results will have the same units as your input. That means the Moment of Inertia I z I x I y. Here is the application of the parallel axis theorem to calculate ly&x27;. The following example finds the centroidal moment of inertia for a rectangle using integration. The moment of inertia of a triangular lamina with respect to an axis passing through its centroid, parallel to its base, is given by the expression where is the base width, and specifically the triangle side parallel to the axis, and is the triangle height (perpendicular to the axis and the base) as shown in the figure. Centroid, Area, Moments of Inertia, Polar Moments of Inertia, & Radius of Gyration of a Triangular Cross-Section. Case I. F m a. So, the vertices of the equilateral triangle are (1 2 a, 3 6 a), (0, 3 3 a), (1 2 a, 3 6 a) Let's calculate the moment of inertia through the center of the plate as if the triangle was laying flat in the x-y plane and the center is the origin, with the z-axis going. 5 31, 2022. The moments of inertia of the plane region about the x- and u-axes are Ix0. The gate weight of 1500 N is assumed at the centroid of the plate, with moment arm 0. For a uniform triangular plate, the moments of inertia are taken to be about the vertical axis passing through the plate's center of mass. The formula calculates the Moment of Inertia of a right triangle of base b and height h in respect to an axis collinear with the base of the triangle (one of the sides. The base of the pyramid has area l w , and sl and sw represent the slant height on the length and slant height on the width. h 2 dA. 559 meters about point A. The current page is about the mass moment of inertia. In other words, area of a rhombus is half the product of its diagonals. MECHANICAL ENGINEERING 12 MOMENT OF INERTIA AREA Mechanical Engineering Ch 12 Moment of Inertia (41 of 97) 2nd Moment of Area Triangle 13 30,798 views May 2, 2017 258 Dislike. 32075 h 4 M A L, where h is the height of the triangle and L is the area. Figure 17. The SI unit of moment of inertia is kg m 2. In other words, area of a rhombus is half the product of its diagonals. 4 m and base angles equal to , with respect to an axis passing through its vertex Relevant Equations moment of inertia I did in this way Dividing the triangle in small rectangles with where we have Now i have. You can calculate the Moments of Inertia Ix, Iy. 5) What is the centroidal distance along the line of symmetry XO for the quarter circle shown below. J g hb 3 6 h2 a2 ab b2 J g h b 3 6 h 2 a 2 a b b 2 This is the final expression for j at the Cg The second method is to get the Polar moment of inertia J for The triangle at the CG. Moment of inertia about the centroidal axis of the triangle Applying parallel axis theorem we get I x x I c c A (h 3) 2 I c c I x x A (h 3) 2 I c c b h 3 12 b h 2 h 2 9 b h 3 36 I c e n t r o i d b h 3 36 Download Solution PDF Share on Whatsapp Latest DFCCIL Junior Manager Updates Last updated on Sep 29, 2022. blackpink song association; washington state high school gymnastics championships 2022; sherri papini story. spoken english course free download vag ecu eeprom calculator. 2 Su2014abn 2 pole o r id y s f t y A dA A B B y d Just like for center of gravity of an area, the moment of inertia can be determined with respect to any reference axis. DERIVATION OF MOMENT OF INERTIA TRIANGLE RIGHT ANGLE ISO-SCALE AT BASE & APEX AT CENTROID. Please use consistent units for all input. The diagonal of a rhombus bisect each other at 90. 5 31, 2022. MOI varies depending on the axis that is chosen. S, T and U are the midpoints of the sides of the triangle PQ, QR and PR, respectively. For the rectangular region, determine (a) the principal moments of inertia and the principal directions at the centroid C; and (b) the moments and products of inertia about the u-v axes. But the moment of inertia of the big triangle can be also split into 4 moments of inertia. Examples of isosceles triangles include the isosceles. 17, 2016 8 likes 12,003 views Download Now Download to read offline Education fast trics to find centroid and moment of inertia sachin chaurasia Follow Advertisement Recommended Chapter 4 krishndesai 9. Length and breadth must be stated in the same unit of measure. That is, for a rectangular object, the moment of inertia about an. with the system of particles about an axis passing through the center of mass of the system and perpendicular to the plane containing them. In geometry, an isosceles triangle (a s s l i z) is a triangle that has at least two sides of equal length. Here the area can be said to be concentrated, analogous to the centre of gravity of a body and its mass. use these formulas and verify the centroid of the triangular region R R . To find the missing vertex, we will use the fact that the. Annulus(Ring) Capsule Circle Circumference Cone Conical Frustum Cube Cylinder Equilateral Triangle Hemisphere Isosceles Triangle Parallelogram Perimeter Polygon Pyramid Rectangle Rectangular Prism Rhombus Sphere Square Stadium Surface Area Triangle Calculator Right Triangular Prism Tube Volume Orthocenter Moment of Inertia Golden Rectangle Centroid. You have a 2D Area in a XY axis. The centroid of any triangle, right triangles included, is the point where the angle bisectors of all three vertices of a triangle intersect. spoken english course free download vag ecu eeprom calculator. Find the centroid of an isosceles triangle whose base is on the x-axis,. Table of Content. Get complete concept after watching this videoTopics covered in playlist of Moment of Inertia Centroid of Various Sections (rectangle, . A thin, uniform plate in the shape of an equilateral triangle hangs from the midpoint of one john deere 5085e operators manual. Let ABC be a right-angled isosceles triangle where AB BC a. The SI unit of moment of inertia is kg m 2. Q The moment of inertia of an area about an axis is equal to the area moment of inertia about a. I MOI of A1 - MOI of A2 I bh 3 12 - bh 3 12 I (50. 1 First Moment and Centroid of a Set of Points. In other words, area of a rhombus is half the product of its diagonals. For point P, we have. How does rotational inertia relate to Newton&39;s 2 law. newsmax female anchors and reporters; desi porn movies. Iz, A, Yc minertia(ASpec) returns the moment of inertia Iz, the total area A, and the centroid Yc of the area. 5 Example Centroid of a L section A1 x (b This is not technically correct and Second Moment of Area should be preferred. Formula Centroid Height 3. The moment of inertia of a triangle with respect to an axis passing through its base, is given by the following expression This can be proved by application of the Parallel Axes Theorem (see below) considering that triangle centroid is located at a distance equal to h3 from base. comDie zweit&228;hnlichste Website ist optimalbeam. The moment of inertia, or more accurately, the second moment of area, is defined as the integral over the area of a 2D shape, of the squared distance from an axis where A is the area of the shape and y the distance of any point inside area A from a given axis of rotation. Find, in terms of a, the distance between C and I. Centroids of areas are useful for a number of situations in the mechanics course sequence, including in the analysis of. The moment of inertia, or more accurately, the second moment of area, is defined as the integral over the area of a 2D shape, of the squared distance from an axis where A is the area of the shape and y the distance of any point inside area A from a given axis of rotation. In engineering use the areas that tend to be of interest are cross sectional areas. T h y. . Find the degree measure of the vertex angle S. For a uniform triangular plate, the moments of inertia are taken to be about the vertical axis passing through the plate's center of mass. AI Recommended . Here Yc is measured from the bottom of the area. None of these. de 2016. The moment of inertia I is a very important term in the calculation of Critical load in Eulers buckling equation. Area 1 2bh. Some important things to remember regarding a beams area moment of inertia are Area moment of inertia is different from the mass moment of inertia; It is also known as the second moment of area. 8k views 57 slides 1 centroids ELIMENG 2. AD 4 cm is the height of triangle ABC. Question 1. Examples of units which are typically adopted are outlined below Notation A Geometric Area, in2or mm2 C Distance to Centroid, in or mm I Second moment of area, in4or mm4 Ji Polar Moment of Inertia, in4or mm4 K Radius of Gyration, in or mm P Perimeter of shape, in or mm S Plastic Section Modulus, in3or mm3. Circumcenter is the center of the circumcircle , which is a circle passing through all three vertices of a triangle. with respect to the centroidal axis parallel to BB, knowing that. The diagonals of a rhombus bisect each other at 90 degrees. 13 In equation form Ix I x&92;mathrm cA d2 or. For a isosceles triangle with base b and height h the surface moment of inertia around tbe z axis is bh336 (considering that our coordinate . An isosceles triangle with vertices has the density distribution . amc theater londonderry nh, free slingo credits
That means the Moment of Inertia I z I x I y. . Moment of inertia of isosceles triangle about centroid
6ft4, respectively. 5 Example Centroid of a L section A1 x (b This is not technically correct and Second Moment of Area should be preferred. Centroid, Area, Moments of Inertia, Polar Moments of Inertia, & Radius of Gyration of a Isosceles Trapezoid Home Calculators Forum Magazines Search Members Membership. Moment of inertia mathImath about a line passing through apex angle and parallel to the base of triangle can be found with the help of parallel axis theorem. 32075 h 4 M A L, where h is the height of the triangle and L is the area. An isosceles triangle has its centroid located somewhere on the line of symmetry that . 1-The moment of inertia for an isosceles triangle Ix is obtained by considering the moment of inertia Ix for a Triangle, which we have obtained earlier an Ix bh312 and radius of gyration Kx2 as Ixareabh312 (0. Let ABC be a right-angled isosceles triangle where AB BC a. 0 d. 1 An engineer claims that flow of SAE 30W oil, at 20C, through a 5-cm-diameter smooth pipe at 1 million Nh, is laminar. 627&215;10 6 mm 4) Ans (1. (1) Moment of inertia of a. For the Isosceles triangle shown to the right, find the moments of inertia, Ix and Iy, about the centroidal axes. The moments of inertia of the plane region about the x- and u-axes are Ix0. Figure 17. To find the missing vertex, we will use the fact that the. Let P, Q and R be the three points which divide the line-segment joining the points A(-2, 2) and B(2, 8) in four equal parts. (b) in four segments (1) a tall rectangle, (2) a right isosceles triangle,. Apex Angle Isosceles Triangle. Note that when using the parallel axis theorem, area is always positive, and the MOI of the hole I 2 is subtracted from I. Iz, A, Yc minertia(ASpec) returns the moment of inertia Iz, the total area A, and the centroid Yc of the area. 2020 Physics Secondary School answered Moment of inertia of an. Suppose that we. 1 Describe the geometry and operation of a human peristaltic PDP which is cherished by every romantic person on earth. Since the shape of the triangle can't be described by one formula, you would have to split the integral into multiple sections. Area of a Rhombus To find the area of a rhombus, we divide the quadrilateral into two equal isosceles triangles using the two diagonals. The unequal side length of an isosceles triangle is. The moment of inertia of a triangle having its axis passing through the centroid and parallel to its base is expressed as; I bh 3 36 Here, b base width and h height. But I don&39;t know how to do that. In General form Moment of Inertia is expressed as I m r2 where, m Sum of the product of the mass. We will get the value for the moment of inertia Iy for an isosceles triangle as Iy (748)hb3, where b is the base while h is the height of the isosceles triangle. Centroid of a Trapezoid Formula. y 2 b h 0 h b h y 2 d y Simplifying, y 2 h 2 y 3 3 0 h y 2 h 2 h 3 3 0 y 2 3 h. colegio sagrado corazon de jesus. I MOI of A1 - MOI of A2 I bh 3 12 - bh 3 12 I (50. Rectangular Area Moments of Inertia. colegio sagrado corazon de jesus. Centroids and Centers of Gravity. The centroid theorem states that the centroid of the triangle is at 23 of the distance from the vertex to the mid-point of the sides. Solution Area of the rhombus 1 2 d 1 d 2. The moment of inertia (MI) of a plane area about an axis normal to the plane is equal to the sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis. CENTROID AND MOMENT OF INERTIA 81 From the above equation we can make the statement that distance of centre of gravity of a body from an axis is obtained by dividing moment of the gravitational forces acting on the body, about the axis, by the total weight of the body. Spinning figure skaters. Moment of inertia. It mainly depends on the distribution of mass around an axis of rotation. The moment of inertia (I) is the capacity of a cross-section to resist bending. The moment of inertia , I, is the rotational equivalent of mass. The moment of inertia relative to centroidal axis x-x, can be found by application of the Parallel Axes Theorem (see below). We compute the center of pressure for both bottom and inverted isosceles triangle using the integral and the formula with the area moment of inertia Ic and . 3, a moment of inertia about an axis passing through the area&39;s centroid is a Centroidal Moment of Inertia. The moments of inertia of the plane region about the x- and u-axes are Ix0. Summing moments about point A gives the required force P M A 0 P(2. The Passage of an Axis via the Centroid. Moment of inertia of a triangle of base B and height H about an Axis passing through its base and parallel to centroidal. Jun 10, 2010 angle sum of a triangle angles at a point angular displacement angular momentum angular motion angular velocity annum(X per annum) X anti-clockwise direction anti-clockwise moment anti-derivative . Let ABC be a right-angled isosceles triangle where AB BC a. It mainly depends on the distribution of mass around an axis of rotation. The moment of inertia relative to the axis z, which is at a distance D from the center of mass along the x -axis, is Expanding the brackets yields The first term is Icm and the second term becomes mD2. The convention is to place a bar over the symbol &92;(I&92;) when the the axis is centroidal. 1 The centroid (marked C) for a few common shapes. For the rectangular region, determine (a) the principal moments of inertia and the principal directions at the centroid C; and (b) the moments and products of inertia about the u-v axes. to x-axis is c p c c I h h h A where 3 36 c W L I is the area moment of inertia for a triangle with respect to the (depth of the) centroid c h. The moment of inertia of a triangle having its axis passing through the centroid and parallel to its base is expressed as; I bh 3 36 Here, b base width and h height 2. So if the moment of inertia of the rectangle is, about its centroid, is bh cubed over 12, and the moment of inertia of the hole, the circle, from the previous tables is pi r to the 4th, over 4. A As per parallel axis theorem The. IT A1. de 2018. The two interior angles that are opposite these sides are equal to each other. Answer Thank you User-12527562540311671895 for A2A The moment of inertia of a triangular lamina with respect to an axis passing through its centroid, parallel to its base, is given by the expression IXX&92;frac136bh3 where b is the base width, and specifically the triangle side parallel. Moment of inertia - Rectangular shapesection (formula) Strong Axis I y 1 12 h 3 w Weak Axis I z 1 12 h 3 w Dimensions of rectangular Cross-section. Where, I is the moment of inertia, dm is the mass of a small element considered on the object, and y is the distance of the elemental mass from the axis. Mechanical Engineering questions and answers. The moment of inertia of a triangle having its axis passing through the centroid and parallel to its base is expressed as; I bh 3 36 Here, b base width and h height. An online moment of inertia calculator is exclusively programmed to determine the moment of inertia of common geometrical figures like triangle, rectangle, and many more. Formula Centroid Height 3. Length and breadth must be stated in the same unit of measure. The following example finds the centroidal moment of inertia for a rectangle using integration. Since the triangle is made up of three rods, hence the moment of inertia of all three rods is given by I 3I 2. A rectangle is having base b and height h. We compute the center of pressure for both bottom and inverted isosceles triangle using the integral and the formula with the area moment of inertia Ic and find that for both triangles. In geometry, an isosceles triangle (assliz) is a triangle that has at least two sides of equal length. Let ABC be a right-angled isosceles triangle where AB BC a. de 2021. Answer Thank you User-12527562540311671895 for A2A The moment of inertia of a triangular lamina with respect to an axis passing through its centroid, parallel to its base, is given by the expression IXX&92;frac136bh3 where b is the base width, and specifically the triangle side parallel. An area with an axis of symmetry will find its first moment of area with respect to that axis is equal to zero i. Jun 10, 2010 angle sum of a triangle angles at a point angular displacement angular momentum angular motion angular velocity annum(X per annum) X anti-clockwise direction anti-clockwise moment anti-derivative . In General form Moment of Inertia is expressed as I m r2 where, m Sum of the product of the mass. We will get the value for the moment of inertia Iy for an isosceles triangle as Iy (748)hb3, where b is the base while h is the height of the isosceles triangle. - The distance &x27;r&x27; from any vertex of the. Apex Angle of Isosceles Triangle. de 2019. Assuming rods to be thin, position of center of mass of each rod is at the center of rod. Parallel axis theorem is used to find a moment of inertia about an axis which is at some distance from the centroidal axis and parallel to . T h y. The equation for polar moment of inertia is essentially the same as that for the planar moment of inertia, but in the case of polar moment, distance is measured to an axis parallel to the areas cross-section, instead of I, but its units are the same as those for the planar moment of inertia i. That means the Moment of Inertia I z I x I y. The centroid of a triangle formula is applied to find the centroid of a triangle using the coordinates of the vertices of a triangle. Maths is always daunting, theres no way around it. . great clips winchester tn