slides - FSU Computer Science
... Graph density and efficient storage A complete graph contains an edge for every pair of vertices On the other extreme, sparse graphs contain much fewer than the O(n2) possible edges ...
... Graph density and efficient storage A complete graph contains an edge for every pair of vertices On the other extreme, sparse graphs contain much fewer than the O(n2) possible edges ...
A tetrahedron is a solid with four vertices, , , , and , and four
... (a) Find a formula for the volume of a tetrahedron in terms of the coordinates of its vertices P, Q, R, and S. (b) Find the volume of the tetrahedron whose vertices are P共1, 1, 1兲, Q共1, 2, 3兲, R共1, 1, 2兲, and S共3, ⫺1, 2兲. 3. Suppose the tetrahedron in the figure has a trirectangular vertex S. (This ...
... (a) Find a formula for the volume of a tetrahedron in terms of the coordinates of its vertices P, Q, R, and S. (b) Find the volume of the tetrahedron whose vertices are P共1, 1, 1兲, Q共1, 2, 3兲, R共1, 1, 2兲, and S共3, ⫺1, 2兲. 3. Suppose the tetrahedron in the figure has a trirectangular vertex S. (This ...
Känguru der Mathematik 2004 - Student
... 6) Each inhabitant of planet Mars has either one, two or three tentacles on their head. Exactly 1% of the population have three 97% have two and 2% have one. How many percent of the population have more tentacles than is the average of the entire ...
... 6) Each inhabitant of planet Mars has either one, two or three tentacles on their head. Exactly 1% of the population have three 97% have two and 2% have one. How many percent of the population have more tentacles than is the average of the entire ...
ABC DEF? DECF?
... Directions: To receive full credit, show all required work and place answers in the space provided, when applicable. 1. This is a regular polygon. Find the value of x and y. ...
... Directions: To receive full credit, show all required work and place answers in the space provided, when applicable. 1. This is a regular polygon. Find the value of x and y. ...
Lekcja 4 B
... The intersection of a straight line Lines and planes are proper subsets of When a regular hexagon is inscribed in a circle The centre of a regular polygon If two distinct lines which are not in the same plane do not intersect, ...
... The intersection of a straight line Lines and planes are proper subsets of When a regular hexagon is inscribed in a circle The centre of a regular polygon If two distinct lines which are not in the same plane do not intersect, ...
Geometry Honors Name
... 10. The measures of the acute exterior angles a right triangle are 3x + 25 and 5x + 5. Find the measures of the angles of the triangle. (Hint – draw a picture!) ...
... 10. The measures of the acute exterior angles a right triangle are 3x + 25 and 5x + 5. Find the measures of the angles of the triangle. (Hint – draw a picture!) ...
Document
... One of the lines that make a flat (2-dimensional) shape. Or one of the surfaces that make a solid (3-dimensional) object. ...
... One of the lines that make a flat (2-dimensional) shape. Or one of the surfaces that make a solid (3-dimensional) object. ...
Unit 1
... Line segment - A straight path joining two points. The two points are called the endpoints of the segment. Parallelogram - A quadrilateral that has two pairs of parallel sides. Opposite sides of a parallelogram have equal lengths. Opposite angles of a parallelogram have the same measure. ...
... Line segment - A straight path joining two points. The two points are called the endpoints of the segment. Parallelogram - A quadrilateral that has two pairs of parallel sides. Opposite sides of a parallelogram have equal lengths. Opposite angles of a parallelogram have the same measure. ...
Section 2.2 part 2
... that one side matches up exactly with the other side. – This line is called the line of symmetry or the axis of symmetry. • Rotation symmetry - if the figure can be turned around a point less than 360 degree and match up. – This point is called the center of rotation. ...
... that one side matches up exactly with the other side. – This line is called the line of symmetry or the axis of symmetry. • Rotation symmetry - if the figure can be turned around a point less than 360 degree and match up. – This point is called the center of rotation. ...
4.11 Curriculum Framework
... The study of geometric figures must be active, using visual images and concrete materials (tools such as graph paper, pattern blocks, geoboards, geometric solids, and computer software tools). ...
... The study of geometric figures must be active, using visual images and concrete materials (tools such as graph paper, pattern blocks, geoboards, geometric solids, and computer software tools). ...
hw8
... All of these, I gave you in class, except for 3.7.42, which just happens to work (you can check it with your formula from problem 1). Note that just because a notation satisfies Rule 1, that doesn’t mean that the notation represents an actual tiling. It has to satisfy all five rules. 4) Finish filli ...
... All of these, I gave you in class, except for 3.7.42, which just happens to work (you can check it with your formula from problem 1). Note that just because a notation satisfies Rule 1, that doesn’t mean that the notation represents an actual tiling. It has to satisfy all five rules. 4) Finish filli ...
Practice C - Elmwood Park Memorial High School
... 3. The pattern is the letters of the alphabet that are made only from straight ...
... 3. The pattern is the letters of the alphabet that are made only from straight ...
Math Notes-chap 1
... The line of reflection ___________ (cuts in half) the line segment connecting each image point with its corresponding point on the original figure. Based on the picture, AP=_____. ...
... The line of reflection ___________ (cuts in half) the line segment connecting each image point with its corresponding point on the original figure. Based on the picture, AP=_____. ...
Geometry glossary Assignment
... homework grades. The points will be determined as follows: 30 points for Part I, 35 points for Part II and 35 points for Part III. The terms should be in the order given on this page. For each term, find the most accurate and complete definition you can, and include a diagram to strengthen the defin ...
... homework grades. The points will be determined as follows: 30 points for Part I, 35 points for Part II and 35 points for Part III. The terms should be in the order given on this page. For each term, find the most accurate and complete definition you can, and include a diagram to strengthen the defin ...
File
... • A 4-sided flat shape with straight sides where all interior angles are right angles (90°). • Also opposite sides are parallel and of equal length. ...
... • A 4-sided flat shape with straight sides where all interior angles are right angles (90°). • Also opposite sides are parallel and of equal length. ...
Unit 1 Almost There
... 15. Theorem: If parallel lines are cut by a transversal then the alternate interior angles are congruent. State the Contrapositive of the theorem. ______________________________________________________________________ ______________________________________________________________________ 16. Given: ...
... 15. Theorem: If parallel lines are cut by a transversal then the alternate interior angles are congruent. State the Contrapositive of the theorem. ______________________________________________________________________ ______________________________________________________________________ 16. Given: ...
Complex polytope
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. On a real line, two points bound a segment. This defines an edge with two bounding vertices. For a real polytope it is not possible to have a third vertex associated with an edge because one of them would then lie between the other two. On the complex line, which may be represented as an Argand diagram, points are not ordered and there is no idea of ""between"", so more than two vertex points may be associated with a given edge. Also, a real polygon has just two sides at each vertex, such that the boundary forms a closed loop. A real polyhedron has two faces at each edge such that the boundary forms a closed surface. A polychoron has two cells at each wall, and so on. These loops and surfaces have no analogy in complex spaces, for example a set of complex lines and points may form a closed chain of connections, but this chain does not bound a polygon. Thus, more than two elements meeting in one place may be allowed.Since bounding does not occur, we cannot think of a complex edge as a line segment, but as the whole line. Similarly, we cannot think of a bounded polygonal face but must accept the whole plane.Thus, a complex polytope may be understood as an arrangement of connected points, lines, planes and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on. Likewise, each line must contain multiple points, each plane multiple lines, and so on.