Euclid$26176$ - ترجمة إلى الهولندية
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Euclid$26176$ - ترجمة إلى الهولندية

CITY IN CUYAHOGA COUNTY, OHIO, UNITED STATES
Euclid, OH; UN/LOCODE:USEUC; Euclid (city, Ohio); Euclid,ohio; Euclid, oh; Euclid, Oh; History of Euclid, Ohio
  • Workers in Euclid during World War II

Euclid      
n. Euclides (Grieks wiskundige, vader van de euclidische meetkunde)
plane geometry         
  • A disproof of Euclidean geometry as a description of physical space. In a 1919 test of the general theory of relativity, stars (marked with short horizontal lines) were photographed during a solar [[eclipse]]. The rays of starlight were bent by the Sun's gravity on their way to Earth. This is interpreted as evidence in favor of Einstein's prediction that gravity would cause deviations from Euclidean geometry.
  • A sphere has 2/3 the volume and surface area of its circumscribing cylinder. A sphere and cylinder were placed on the tomb of Archimedes at his request.
  • Congruence of triangles is determined by specifying two sides and the angle between them (SAS), two angles and the side between them (ASA) or two angles and a corresponding adjacent side (AAS). Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles unless the angle specified is a right angle.
  • invariant]]s and studying them is the essence of geometry.
  • René Descartes. Portrait after [[Frans Hals]], 1648.
  • The parallel postulate (Postulate 5): If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
  • Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized [[compass and straightedge]].
MATHEMATICAL SYSTEM ATTRIBUTED TO EUCLID
Geometry in R2; Euclid's postulates; Plane Geometry; Euclidean Geometry; Euclidian geometry; Geometry Postulates; Two dimensional geometry; Two-dimensional geometry; Noncoordinate geometry; Orthogonal geometry; Euclid's axioms; Euclidean geometry of the plane; Euclid axioms; Euclid postulates; Euclidean axioms; Axioms of geometry; Euclidean plane geometry; Fundamental concepts of geometry; Plane geometry; Classical geometry; Planar geometry; Geometry of Euclid; Euclid's second postulate; Euclid's third postulate; Euclid's fourth postulate; Applications of Euclidean geometry; 2D geometry
vlakke meetkunde
Pythagorean theorem         
  • Rearrangement proof of the Pythagorean theorem.<br>(The area of the white space remains constant throughout the translation rearrangement of the triangles.  At all moments in time, the area is always '''''c²'''''.  And likewise, at all moments in time, the area is always '''''a²+b²'''''.)
  • Geometric proof of the Pythagorean theorem from the ''[[Zhoubi Suanjing]]''
  • The absolute value of a complex number ''z'' is the distance ''r'' from ''z'' to the origin.
  • '''a × b'''}} is normal to this plane.
  • Right triangle on the hypotenuse dissected into two similar right triangles on the legs, according to Einstein's proof.
  • The [[spiral of Theodorus]]: A construction for line segments with lengths whose ratios are the square root of a positive integer
  • [[Hyperbolic triangle]]
  • Proof in Euclid's ''Elements''
  • Illustration including the new lines
  • Showing the two congruent triangles of half the area of rectangle BDLK and square BAGF
  • (r<sub>2</sub>, θ<sub>2</sub>)}} in [[polar coordinates]] is given by the [[law of cosines]]. Interior angle Δθ = θ<sub>1</sub>−θ<sub>2</sub>.
  • Distance between infinitesimally separated points in [[Cartesian coordinates]] (top) and [[polar coordinates]] (bottom), as given by Pythagoras' theorem
  • Vectors involved in the parallelogram law
  • p=36}}.</ref>
  • Animation showing proof by rearrangement of four identical right triangles
  • Diagram for differential proof
  • Animation showing another proof by rearrangement
  • Pythagoras' theorem in three dimensions relates the diagonal AD to the three sides.
  • Diagram of the two algebraic proofs
  • A + B {{=}} blue}} area C
  • Generalization for regular pentagons
  • Pythagoras' theorem using similar right triangles
  • Construction for proof of parallelogram generalization
  • area {{=}} blue}} area
  • Proof using similar triangles
  • Proof using an elaborate rearrangement
  • A tetrahedron with outward facing right-angle corner
  • Spherical triangle
  • Similar right triangles showing sine and cosine of angle θ
  • publisher=Mathematical Association of America}}

</ref> Lower panel: reflection of triangle CAD (top) to form triangle DAC, similar to triangle ABC (top).
  • Visual proof of the Pythagorean theorem by area-preserving shearing
RELATION IN EUCLIDEAN GEOMETRY AMONG THE THREE SIDES OF A RIGHT TRIANGLE
PythagoreanTheorem; Pythagorean Theorm; Pythagoras' Theorem; Pythagoras' theorem; Pythagorean Theorem; Pythagoras theorem; Pythagorean Theorum; Pythagoras' Theorem Proof; Pythagoras's Law; Pythagoras’ theorem; Pythagoras’ Theorem; Pythagorean theorum; Pythagorean equation; A² + b² = c²; A²+b²=c²; A2 + b2 = c2; A2+b2=c2; Pythagoras's theorem; Pythagorus's theorem; Pythagorus's theorum; Pythagoras's theorum; The Pythagorean theorem; Pythagorus' theorum; Pythagoras theory; Pythagorean Thm; Theorem of Pythagoras; 47th Problem of Euclid; Pythagorean theorem proof; Pythagoras Theorem; A^2+b^2=c^2; Pyth. thm; Pyth. theorem; Converse of Pyth. thm; Converse of Pyth. theorem; Pythagorean formula; Pythagorean theory; Gougu theorem; Gougu; Pythagoras' law; Gougu's Theorem; Generalizations of the Pythagorean theorem
wet van Pythagoras

تعريف

Euclid
·noun A Greek geometer of the 3d century ·b.c.; also, his treatise on geometry, and hence, the principles of geometry, in general.

ويكيبيديا

Euclid, Ohio

Euclid is a city in Cuyahoga County, Ohio, United States. It is an inner ring suburb of Cleveland. The population was 49,692 at the 2020 census, making it the fourth largest city in Cuyahoga County, behind Cleveland, Parma and Lakewood.