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Dynamic shelter structure
Published in Paulo J.S. Cruz, Structures and Architecture: Bridging the Gap and Crossing Borders, 2019
F. Maden, D. Ölmez, Ş. Gür, M.Y. Uncu, C. Mitropoulou
The loop types are identified based on the quadrilaterals. In Euclidean plane geometry, a quadrilateral is defined as a four-sided polygon with four vertices (Johnson 1929) which has three topological types as convex, concave and crossed quadrilaterals (Fig. 2a). Interior angles measure less than 180° in convex quadrilateral whereas one interior angle exceeds 180° in concave quadrilateral. On the other hand, the sum of the interior angles on both sides of the crossing are equal in crossed quadrilateral. Rhombus, square, rectangle, parallelogram, kite, dart and trapezoid are the basic geometric shapes that fall under the quadrilateral category (Fig. 2b). Using these shapes, different types of scissor loops can be generated.
Two-Dimensional Quadrilateral Element
Published in Darrell W. Pepper, Juan C. Heinrich, The Finite Element Method, 2017
Darrell W. Pepper, Juan C. Heinrich
The quadrilateral element is a four-sided polygon. The most commonly used shapes contain four nodes located at the vertices and are bilinear in a rectangular configuration. Other commonly used rectangular elements involve 8-noded quadratics, 9-noded biquadratics, and 12-noded cubic configurations. Originally, the finite element method used triangular elements exclusively. However, many researchers now prefer quadrilateral elements. In the bilinear approximation, quadrilateral elements add one more node, compared to only three nodes for the triangle. In addition, gradients are linear functions of the coordinate directions, compared to the gradients being constant in triangular element. For higher-order elements, more complex representations are achieved that are increasingly more accurate from an approximation point of view. However, care must be taken to evaluate the benefits of increased accuracy against the increased computational cost associated with more sophisticated elements.
Triangles and quadrilaterals
Published in James Kidd, Ian Bell, Maths for the Building Trades, 2014
A quadrilateral is a figure bounded by four straight lines. It can be split into two triangles with a diagonal line. The sum of the four angles in a quadrilateral is 360°. If three of the angles are known the fourth can be found.
A comparison of mathematical features of Turkish and American textbook definitions regarding special quadrilaterals
Published in International Journal of Mathematical Education in Science and Technology, 2019
Textbook analysis studies have dealt with a quite limited range of mathematical content topics such as whole number addition and subtraction (e.g. [8]), whole number multiplication and division (e.g. [9]), decimals (e.g. [10]), integer addition and subtraction (e.g. [11]), representation of fractions (e.g. [12]), fraction addition and subtraction (e.g. [4]), and fraction multiplication and division (e.g. [7,13]). Although the topic of special quadrilaterals is crucial, it has received only some attention in textbook analysis studies (e.g. [14]). Thereby, in this study, I focused on definitions of special quadrilaterals presented in the US and Turkish school mathematics textbooks. It is important to note that, in this study, the term ‘quadrilateral’ refers to a closed four-sided figure with line segments as sides, no three vertices collinear, and all vertices in a plane as defined by Pereira-Mendoza [15] and the term ‘special quadrilateral’ refers to a quadrilateral with special properties that distinguish it from other quadrilaterals. The particular special quadrilaterals that were examined within the scope of this study are a trapezium, a parallelogram, a rectangle, a square, a kite, and a rhombus.
Necessary and sufficient properties for a cyclic quadrilateral
Published in International Journal of Mathematical Education in Science and Technology, 2020
David Fraivert, Avi Sigler, Moshe Stupel
Throughout this section (up to Subsection 5.3), ABCD is a convex quadrilateral in which , E is the point of intersection of the diagonals, F is the point of intersection of the extensions of sides BC and AD, and ω is some circle that passes through points E and F and through interior points of sides BC and AD (we denote them by M and N, respectively), and let and (see Figure 21). ‘Pascal points on the sides of a quadrilateral’, ‘circle that forms Pascal points’.For the geometric situation described in the general datum, the following property holds (see Fraivert, 2016a, 2016b): Straight lines KN and LM intersect at point P, which lies on side AB and straight lines KM and LN intersect at point Q, which lies on side CD (see Figure 21).Circle ω is termed ‘a circle that forms Pascal points on sides AB and CD’.The points P and Q are termed ‘Pascal points formed by the circle ω’.Complete quadrilateral.A complete quadrilateral is a shape obtained from an ordinary quadrilateral (in which the opposite sides are not parallel) by continuing the opposite sides up to the point of their intersection. A complete quadrilateral has three pairs of opposite vertices. Two opposite pairs are the two pairs of opposite vertices in the original quadrilateral, and the additional opposite pair is the two points of intersection of the extensions of the sides. The line that passes through a pair of opposite vertices is called a diagonal of the complete quadrilateral (see Hadamard, 2008, Section 145).In complete quadrilateral AFBECD (which is obtained from the regular quadrilateral AFBE, see Figures 22 and 23), AB, CD, and EF are diagonals.