5 parallelism
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Parallelism refers to two or more lines or planes in Euclidean space that do not intersect. Euclid's parallel postulate states that given a line and a point not on the line, there is exactly one line through the point that is parallel to the given line. Two lines are parallel if they remain an equal distance apart and never intersect. In elliptic geometry on a sphere, all lines are great circles that intersect, so there are no parallel lines. In hyperbolic geometry using the Poincare disc model, lines are represented by arcs of circles orthogonal to the boundary circle.
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Term Paper Coordinate Geometry
The document provides a summary of coordinate geometry. It begins with definitions of key terms like the coordinate plane, axes, quadrants, and coordinates. It then discusses finding the midpoint, distance, and section formula between two points. Methods for finding the coordinates of the centroid and area of a triangle are presented. The document outlines different forms of equations for straight lines, including their slopes and the general equation of a line. It concludes with some uses of coordinate geometry, such as determining if lines are parallel/perpendicular.
What term best describes the map that presents shape but does no.docx
What term best describes the map that presents shape but does not maintain correct area relationships?
gnomonic
equivalent
conformal
tangent
compromise
What term refers to a latitude line where the map is tangent to Earth?
great circle
transverse Mercator
gnomonic
Interrupted
standard parallel
Which family of map projections is usually tangent at the equator with the projection surface parallel to Earth's axis?
conic
planar
transverse
pseudocylindrical
cylindrical
Which statement best describes a transverse Mercator projection?
most parallels are straight
most meridians are curved lines
an equal area projection
a compromise projection
tangent to the equator
What term describes a straight line of constant direction that crosses all meridians at the same angle?
graticule
great circle
tangent
standard parallel
rhumb line
Which statement describes a Mercator projection?
High latitude areas are exaggerated in size.
Meridians converge to the poles.
Parallels and meridians meet at different angles.
The North and South Poles are points.
The map shape is circular.
Which statement describes an Eckert IV projection?
The shape is rectangular.
The map is an equivalent projection.
Parallels are curved.
The direction north is always straight toward the top of the map
.Parallels and meridians all cross at right angles
Which statement describes the Goode's Interrupted Homolosine projection?
It is interrupted, because major areas of Earth are “left off†and not mapped.
A different projection is used for the Eastern Hemisphere than the Western Hemisphere.
It is a compromise projection.
The shape of the parallels are circles.
It is an equivalent projection.
Which projection is noted for showing great circle routes as straight lines?
Goode's Interrupted Homolosine
Mercator
Lambert Conformal Conic
Robinson
Gnomonic
Which map projection is suitable for showing global densities of certain values such as population or worldwide distribution of earthquakes?
Eckert IV
Lambert Conformal Conic
Gnomonic
Robinson
Mercator
...
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"Euclid" - 'The Father Of Geometry'
The Presentation explains 'The Father Of Geometry' - "Euclid" with his life history and some of his most influential and remarkable works which contribute to The Modern Mathematics.
euclid geometry
Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". His influential work Elements laid out the principles of geometry and served as the main geometry textbook from its publication until the 19th century. Elements deduced geometric principles from a small set of axioms and also covered number theory. Euclid wrote extensively on geometry, including dimensions, angles, curves, and shapes in two and three dimensions. He also wrote works on optics, perspective, and conic sections that investigated the apparent sizes of objects at different distances and angles.
Euclid’s geometry
Geometry is a branch of mathematics concerned with questions of shape, size, position, and space. A key figure was the Greek mathematician Euclid, whose book Elements systematized geometry in the 3rd century BC. Euclid defined fundamental terms like point and line, and postulated axioms and rules for reasoning about geometric concepts. Euclid's system of Euclidean geometry reigned for over 2000 years, until non-Euclidean geometries emerged in the 19th century challenging its assumptions about physical space.
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What term best describes the map that presents shape but does no.docx
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5 parallelism
- 1. Parallelism is a term in geometry that refers to a propiety in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of euclid’s parallel postulate. Two lines in a plane that do not intersect or tuch at a point are called parallel lines.
- 2. Eucliden Parallelism • Given straight lines / and m, the following description of line m equivalently define it as parallel to line / in Euclidean space: • Lines m and / are both intersected by a third straight line ( a trasversal ) in the same plane, and corresponding angles of intersection whit the trasversal are equal. ( this is equivalent to euclid’s parallel postulate).
- 3. Ellictical geometry In the spherical plane, all geodesics are great circles. Great circles divide the sphere in two equal hemispheres and all great circles intersect each other. Equidistant line on the sphere are called parallels of latitude in analog to latitude lines on a globe.
- 4. Hyperbolic geometry • The Poincare disc model, also know as the conformal disc model, also employs the interior of a circle, but lines are rapresented by arcs of a circles that are orthogonal to the boundary circle, plus diameters of the boundary circle.
- 5. Perpendicular • In geometry, two lines or planes ( or a lines and a plane ) are considered perpendicular ( or orthogonal ) to each other if they form congruent adjacent angles.
- 6. REALIZZATO DA ABBONDANZA MARCO BORRACINO SIMONE LOZITO ALESSANDRO MALLARDI SABINO PARADISO LORENZO