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Triangle - Computing the area of a triangle | A Wisdom Archive on Triangle - Computing the area of a triangle | | Triangle - Computing the area of a triangle A selection of articles related to Triangle - Computing the area of a triangle | |
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Triangle, Triangle - Basic facts, Triangle - Computing the area of a triangle, Triangle - Non-planar triangles, Triangle - Points, lines and circles associated with a triangle, Triangle - Types of triangles, Triangle - Using Heron's formula, Triangle - Using coordinates, Triangle - Using geometry, Triangle - Using the side lengths and a numerically stable formula, Triangle - Using trigonometry, Triangle - Using vectors
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ARTICLES RELATED TO Triangle - Computing the area of a triangle | |
| | |  Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Computing the area of a triangle
Calculating the area of a triangle is an elementary problem encountered often in many different situations. Various approaches exist, depending on what is known about the triangle. What follows is a selection of frequently used formulae for the area of a triangle.
Triangle - Using geometry.
The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base. ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Computing the area of a triangle |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Computing the area of a triangle Calculating the area of a triangle is an elementary problem encountered often in many different situations. Various approaches exist, depending on what is known about the triangle. What follows is a selection of frequently used formulae for the area of a triangle.
Triangle - Using geometry.
The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base. ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Computing the area of a triangle |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Points, lines and circles associated with a triangle There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points, lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Points, lines and circles associated with a triangle |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Sierpinski triangle - Properties The Sierpinski triangle has Hausdorff dimension log(3)/log(2) ≈ 1.585, which follows from the fact that it is a union of three copies of itself, each scaled by a factor of 1/2.
If one takes Pascal's triangle with 2n rows and colors the even numbers white, and the odd numbers black, the result is an approximation to the Sierpinski triangle.
The area of a Sierpinski triangle is zero (in Lebesgue measure). This can been seen from the infinite iteration, where we remo ...
See also:Sierpinski triangle, Sierpinski triangle - Construction, Sierpinski triangle - Properties, Sierpinski triangle - Analogs in higher dimension, Sierpinski triangle - Self-assembly with DNA, Sierpinski triangle - Computer Program Read more here: » Sierpinski triangle: Encyclopedia II - Sierpinski triangle - Properties |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Tetrahedron - The isometries of irregular tetrahedra An irregular tetrahedron (3-sided Pyramid (geometry)) with equilateral base and the top vertex above the center has 6 isometries, like an equilateral triangle.
A tetrahedron composed of two pairs of identical isoceles triangles is such that the two edges that adjoin identical triangles are opposite and perpendicular, and thus such a tetrahedron (or digonal disphenoid) has one twofold rotational axis passing through the centers of the two edges that adjoin identical triangles (in the case where all four triangles are identical and the ...
See also:Tetrahedron, Tetrahedron - Area and volume, Tetrahedron - Geometric relations, Tetrahedron - Related polyhedra, Tetrahedron - Intersecting tetrahedra, Tetrahedron - The isometries of the regular tetrahedron, Tetrahedron - The isometries of irregular tetrahedra, Tetrahedron - Computational uses, Tetrahedron - Trivia Read more here: » Tetrahedron: Encyclopedia II - Tetrahedron - The isometries of irregular tetrahedra |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Indian mathematics - Vedic Mathematics 1500 BC - 500 BC As a result of the mathematics required for the construction of religious altars, many rules and developments of geometry are found in Vedic works, along with many astronomical developments for religious purposes. These include the use of geometric shapes, including triangles, rectangles, squares, trapezia and circles, equivalence through numbers and area, squaring the circle and visa-versa, the Pythagorean theorem and Pythagorean triples, and computations of π.
Vedic works also contain all four arithmetical operators (addition, subt ...
See also:Indian mathematics, Indian mathematics - Indian contributions to mathematics, Indian mathematics - Harappan Mathematics 3300 BC - 1700 BC, Indian mathematics - Vedic Mathematics 1500 BC - 500 BC, Indian mathematics - Vedas 1500 BC - 500 BC, Indian mathematics - Samhitas 1500 BC - 500 BC, Indian mathematics - Lagadha 1350 BC - 800 BC, Indian mathematics - Yajnavalkya 1000 BC - 600 BC, Indian mathematics - Sulba Sutras 800 BC - 500 BC, Indian mathematics - Ancient Period 500 BC - 400 CE, Indian mathematics - Panini 500 BC - 400 BC, Indian mathematics - Pingala 400 BC - 200 BC, Indian mathematics - Vaychali Ganit 300 BC - 200 BC, Indian mathematics - Katyayana 200 BC, Indian mathematics - Jaina Mathematics 400 BC - 400 CE, Indian mathematics - Surya Siddhanta 300 CE - 400 CE, Indian mathematics - Classical Period 400 CE - 1200 CE, Indian mathematics - Aryabhata I 476-550, Indian mathematics - Bhaskara I 600-680, Indian mathematics - Brahmagupta 598-668, Indian mathematics - Shridhara Acharya 650-850, Indian mathematics - Mahavira Acharya 850, Indian mathematics - Aryabhata II 920-1000, Indian mathematics - Shripati Mishra 1019-1066, Indian mathematics - Nemichandra Siddhanta Chakravati 1100, Indian mathematics - Bhaskara Acharya Bhaskara II 1114-1185, Indian mathematics - Keralese Mathematics 1300 CE -1600 CE, Indian mathematics - Narayana Pandit 1340-1400, Indian mathematics - Madhava of Sangamagramma 1340-1425, Indian mathematics - Parameshvara 1370-1460, Indian mathematics - Nilakantha Somayaji 1444-1544, Indian mathematics - Jyesthadeva 1500-1575, Indian mathematics - Charges of Eurocentrism Read more here: » Indian mathematics: Encyclopedia II - Indian mathematics - Vedic Mathematics 1500 BC - 500 BC |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Points lines and circles associated with a triangle There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Points lines and circles associated with a triangle |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Points lines and circles associated with a triangle There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Points lines and circles associated with a triangle |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Basic facts Elementary facts about triangles were presented by Euclid in books 1-4 of his Elements around 300 BCE.
A triangle is a polygon and a 2-simplex (see polytope). All triangles are two-dimensional.
Two triangles are said to be similar if and only if the angles of one are equal to the corresponding angles of the other. In this case, the lengths of their corresponding sides are proportional. This occurs for example when two triangles share an angle and the si ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Basic facts |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Types of triangles Triangles can be classified according to the relative lengths of their sides:
In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon
In an isosceles triangle two sides are of equal length. An isosceles triangle also has two equal internal angles (namely, the angles where each of the equal sides meets the third side).
In a scalene triangle all sides have different lengths. The internal angles ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Types of triangles |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Basic facts Elementary facts about triangles were presented by Euclid in books 1-4 of his Elements around 300 BCE.
A triangle is a polygon and a 2-simplex (see polytope).
Two triangles are said to be similar if and only if the angles of one are equal to the corresponding angles of the other. In this case, the lengths of their corresponding sides are proportional. This occurs for example when two triangles share an angle and the sides opposite to that angle are parallel.
Using right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Basic facts |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Types of triangles Triangles can be classified according to the relative lengths of their sides:
In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon
In an isosceles triangle two sides are of equal length. An isosceles triangle also has two equal internal angles (namely, the angles where each of the equal sides meets the third side).
In a scalene triangle all sides have different lengths. The internal angles ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Types of triangles |
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| | | | Triangle - Computing the area of a triangle: Encyclopedia II - Triangle - Basic facts Elementary facts about triangles were presented by Euclid in books 1-4 of his Elements around 300 BCE.
A triangle is a polygon and a 2-simplex (see polytope).
Two triangles are said to be similar if and only if the angles of one are equal to the corresponding angles of the other. In this case, the lengths of their corresponding sides are proportional. This occurs for example when two triangles share an angle and the sides opposite to that angle are parallel.
Using right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle ...
See also:Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Non-planar triangles Read more here: » Triangle: Encyclopedia II - Triangle - Basic facts |
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