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Principle in compass and straightedge constructions
In geometry, the compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these
Compass_equivalence_theorem
Topics referred to by the same term
Compass equivalence theorem, a theorem in straightedge and compass construction Equivalence principle, in general relativity Lax equivalence theorem,
Equivalence_theorem
Theorem in Euclidean geometry
theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. This theorem refers
Mohr–Mascheroni_theorem
Method of drawing geometric objects
transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might
Straightedge and compass construction
Straightedge_and_compass_construction
Mathematics taught in primary and secondary school
a distance can be transferred even with a collapsing compass, see compass equivalence theorem.) More formally, the only permissible constructions are
Elementary_mathematics
Mathematical model of the physical space
intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which relates to parallel
Euclidean_geometry
Number divisible only by 1 and itself
requirements of a valuation. According to Ostrowski's theorem, up to a natural notion of equivalence, the real numbers and p {\displaystyle p} -adic numbers
Prime_number
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making
Arrow's_impossibility_theorem
Algebraic structure with addition, multiplication, and division
proofs that angle trisection and squaring the circle cannot be done with a compass and straightedge alone. Galois theory, devoted to understanding the symmetries
Field_(mathematics)
Simple curve of Euclidean geometry
steps with compass and straightedge. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves
Circle
Curve where spinning and moving lines cross
into n {\displaystyle n} equal parts with ruler and compass is possible due to the intercept theorem. In more detail, to divide a given angle ∠ B A E {\displaystyle
Quadratrix_of_Hippias
Category of mathematical proof
In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as
Proof_of_impossibility
Construction of an angle equal to one third a given angle
only two tools: an unmarked straightedge and a compass. It is a classical problem of straightedge and compass construction of ancient Greek mathematics. In
Angle_trisection
Number constructible via compass and straightedge
equivalence between the algebraic and geometric definitions of constructible numbers has the effect of transforming geometric questions about compass
Constructible_number
Axiom set used in first-order logic
is also complete. This does not contradict Gödel's first incompleteness theorem, because Tarski's theory lacks the expressive power needed to interpret
Tarski's_axioms
Measure of algorithmic complexity
impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a
Kolmogorov_complexity
Relation used in geometry
thus fails to be an equivalence relation. Nevertheless, in affine geometry a pencil of parallel lines is taken as an equivalence class in the set of lines
Parallel_(geometry)
Line which touches a circle at exactly one point
circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs
Tangent_lines_to_circles
Geometry without using coordinates
Butterfly theorem, Angle bisector theorem, Apollonius' theorem, British flag theorem, Ceva's theorem, Equal incircles theorem, Geometric mean theorem, Heron's
Synthetic_geometry
Branch of mathematics
geometry emphasize different invariants and notions of equivalence, such as Morita equivalence. Some of the operator-algebraic constructions used in noncommutative
Noncommutative_geometry
Branch of mathematics
on surfaces, and predicting Einstein's fundamental observation of the equivalence principle a full 60 years before it appeared in the scientific literature
Differential_geometry
Mathematical idealization of the trace left by a moving point
description of the real points into 'ovals'. The statement of Bézout's theorem showed a number of aspects which were not directly accessible to the geometry
Curve
Study of complex manifolds and several complex variables
analytic variety is equivalent to the study of algebraic data. This equivalence indicates that complex geometry is in some sense closer to algebraic
Complex_geometry
Branch of mathematics
theory. Wiles' proof of the longstanding conjecture called Fermat's Last Theorem is an example of the power of this approach. In classical algebraic geometry
Algebraic_geometry
Part of a straight line that is bounded by two distinct end points
pair having the same length and orientation. This application of an equivalence relation was introduced by Giusto Bellavitis in 1835. Analogous to straight
Line_segment
Property of objects which are scaled or mirrored versions of each other
are: the angle bisector theorem, the geometric mean theorem, Ceva's theorem, Menelaus's theorem and the Pythagorean theorem. Similar triangles also provide
Similarity_(geometry)
British physicist, engineer and mathematician (1824–1907)
Thomson. He had extensive maritime interests and worked on the mariner's compass, which previously had limited reliability. Kelvin was ennobled in 1892
Lord_Kelvin
Euclidean geometry without distance and angles
then AC is parallel to A'C'. The affine concept of parallelism forms an equivalence relation on lines. Since the axioms of ordered geometry as presented
Affine_geometry
Non-Euclidean geometry
excess over 180 degrees can be made arbitrarily small. The Pythagorean theorem fails in elliptic geometry. In the 90°–90°–90° triangle described above
Elliptic_geometry
German-born theoretical physicist (1879–1955)
also made important contributions to quantum theory. His mass–energy equivalence formula E = mc2, which arises from special relativity, has been called
Albert_Einstein
Concept in classical electromagnetism
that an electric current produces a magnetic effect. He observed that a compass needle placed near a current-carrying wire deflected so that it aligned
Ampère's_circuital_law
Algorithm for computing greatest common divisors
it can be used as a basic tool for proving theorems in number theory such as Lagrange's four-square theorem and the uniqueness of prime factorizations
Euclidean_algorithm
Integral transform in mathematics
D(\mathbf {P} ^{\vee ,d}).} The main theorem about this transform is that this transform induces an equivalence of the categories of perverse sheaves
Radon_transform
Israeli economist
means" or "overtaking" criteria, proving what is known as the Perfect Folk Theorem. The Email Game: His paper demonstrates that a game with incomplete information
Ariel_Rubinstein
Israeli psychologist (1937–1996)
on anything that was not destined to matter. He also had an unfailing compass that always kept him going forward. Tversky's 1974 Science article with
Amos_Tversky
Thermodynamical parameter of solids
was formulated in terms of the phonon nonlinearities. Because of the equivalences of many properties and derivatives within thermodynamics (e.g. see Maxwell
Grüneisen_parameter
Historical development of physics
trajectory forming one of the legs. On the hypotenuse, Leonardo noted the equivalence of the two orthogonal motions, one effected by gravity and the other
History_of_physics
needle compass and by the 12th century Chinese were known to use the lodestone compass for navigation. In Europe, the first description of the compass and
History of electromagnetic theory
History_of_electromagnetic_theory
asymptotically as it approaches the speed of light. The mass-energy equivalence equation is thus more accurately expressed as E=γmc², where γ is a variable
List of common misconceptions about science, technology, and mathematics
List_of_common_misconceptions_about_science,_technology,_and_mathematics
Property of space that quantifies the magnetic influence at a given location
his own successful model of magnetism in 1825. In it, he showed the equivalence of electrical currents to magnets and proposed that magnetism is due
Magnetic_field
Type of formal logic
provably symmetric and transitive as well. Hence for models of S5, R is an equivalence relation, because R is reflexive, symmetric and transitive. We can prove
Modal_logic
Star at the centre of the Solar System
essential clue to the source of the Sun's energy output with his mass–energy equivalence relation E = mc2. In 1920, Sir Arthur Eddington proposed that the pressures
Sun
Term in educational psychology
S2CID 14318417. Urcuioli, Peter J. (2009-04-08). "Responses and Acquired Equivalence Classes". Comparative Cognition Experimental Explorations of Animal Intelligence
Concept_learning
Relativistic effect due to rotation
light around a massive body. Under general relativity, there is the equivalence principle which states that gravity and acceleration are equivalent.
Sagnac_effect
radar system by Christian Hülsmeyer (Telemobiloscope) 1905: Mass–energy equivalence (E = mc2) and special relativity by Albert Einstein 1905: Rubens tube
List of German inventions and discoveries
List_of_German_inventions_and_discoveries
physicist, best known for his theory of relativity and the mass–energy equivalence, E = m c 2 {\displaystyle E=mc^{2}} John Ericsson (1803–1889): Swedish-American
List_of_agnostics
Mechanism for regulating the speed of clocks
exactly proportional to their mass (inertia). This principle, called the equivalence principle, confirmed to greater accuracy in later experiments, became
Pendulum
Formal model in concurrency theory
N.; Yantchev, Jay (1996). "ARC – a tool for efficient refinement and equivalence checking for CSP". IEEE Int. Conf. on Algorithms and Architectures for
Communicating sequential processes
Communicating_sequential_processes
Contribution 1088 Shen Kuo First person to write of the magnetic needle compass and that it improved the accuracy of navigation by helping to employ the
Timeline of physical chemistry
Timeline_of_physical_chemistry
93×1012 km, 11.76×1012 mi). c. 210 BCE – Apollonius of Perga shows the equivalence of two descriptions of the apparent retrograde planet motions (assuming
Timeline of Solar System astronomy
Timeline_of_Solar_System_astronomy
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