Pythagoras's Theorem - определение. Что такое Pythagoras's Theorem
Diclib.com
Словарь ChatGPT
Поиск в словаре Индивидуальные решения
Введите слово или словосочетание на любом языке 👆
Язык:

Перевод и анализ слов искусственным интеллектом ChatGPT

На этой странице Вы можете получить подробный анализ слова или словосочетания, произведенный с помощью лучшей на сегодняшний день технологии искусственного интеллекта:

  • как употребляется слово
  • частота употребления
  • используется оно чаще в устной или письменной речи
  • варианты перевода слова
  • примеры употребления (несколько фраз с переводом)
  • этимология
  1. Словари
  2. Английский словарь
  3. Pythagoras's Theorem

Что (кто) такое Pythagoras's Theorem - определение

THEOREM
Lob's Theorem; Löb's Theorem; Lob's theorem; Loeb's theorem; Loeb theorem; Lob theorem; Löb theorem; Loeb's Theorem
Найдено результатов: 1938
Pythagoras's 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
<mathematics> The theorem of geometry, named after Pythagoras, of Samos, Ionia, stating that, for a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. I.e. if the longest side has length A and the other sides have lengths B and C (in any units), A^2 = B^2 + C^2 (2004-02-12)
Pythagoras' 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
<spelling> It's Pythagoras's Theorem. (2007-06-07)
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
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
https://en.wikipedia.org/wiki/Pythagorean_theorem
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
Pythagoras's Theorem
Pythagoras' 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
¦ noun the theorem that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Divergence theorem         
  • n}}
  • A volume divided into two subvolumes. At right the two subvolumes are separated to show the flux out of the different surfaces.
  • The volume can be divided into any number of subvolumes and the flux out of ''V'' is equal to the sum of the flux out of each subvolume, because the flux through the <span style="color:green;">green</span> surfaces cancels out in the sum. In (b) the volumes are shown separated slightly, illustrating that each green partition is part of the boundary of two adjacent volumes
  • </math> approaches <math>\operatorname{div} \mathbf{F}</math>
  • The divergence theorem can be used to calculate a flux through a [[closed surface]] that fully encloses a volume, like any of the surfaces on the left. It can ''not'' directly be used to calculate the flux through surfaces with boundaries, like those on the right. (Surfaces are blue, boundaries are red.)
  • The vector field corresponding to the example shown. Vectors may point into or out of the sphere.
GENERALIZATION OF THE FUNDAMENTAL THEOREM IN VECTOR CALCULUS
Gauss' theorem; Gauss's theorem; Gauss theorem; Ostrogradsky-Gauss theorem; Ostrogradsky's theorem; Gauss's Theorem; Divergence Theorem; Gauss' divergence theorem; Ostrogradsky theorem; Gauss-Ostrogradsky theorem; Gauss Ostrogradsky theorem; Gauss–Ostrogradsky theorem
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.
https://en.wikipedia.org/wiki/Divergence_theorem
theorem         
  • planar]] map with five colors such that no two regions with the same color meet. It can actually be colored in this way with only four colors. The [[four color theorem]] states that such colorings are possible for any planar map, but every known proof involves a computational search that is too long to check by hand.
  • universality]]) resembles the [[Mandelbrot set]].
  • strings of symbols]] may be broadly divided into [[nonsense]] and [[well-formed formula]]s. A formal language can be thought of as identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.
IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED
Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem
n.
Proposition (to be demonstrated), position, dictum, thesis.
Well-ordering theorem         
SET-THEORETIC THEOREM OR PRINCIPLE, EQUIVALENT TO THE AXIOM OF CHOICE
Well ordering theorem; Zermelo's well-ordering theorem; Wellordering theorem; Zermelo's theorem; Zermelo Theorem
In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering.
https://en.wikipedia.org/wiki/Well-ordering_theorem
Wedderburn's little theorem         
In mathematics, Wedderburn's little theorem states that every finite domain is a field. In other words, for finite rings, there is no distinction between domains, division rings and fields.
https://en.wikipedia.org/wiki/Wedderburn's_little_theorem
Theorem         
  • planar]] map with five colors such that no two regions with the same color meet. It can actually be colored in this way with only four colors. The [[four color theorem]] states that such colorings are possible for any planar map, but every known proof involves a computational search that is too long to check by hand.
  • universality]]) resembles the [[Mandelbrot set]].
  • strings of symbols]] may be broadly divided into [[nonsense]] and [[well-formed formula]]s. A formal language can be thought of as identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.
IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED
Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem
·vt To formulate into a theorem.
II. Theorem ·noun A statement of a principle to be demonstrated.
III. Theorem ·noun That which is considered and established as a principle; hence, sometimes, a rule.

Википедия

Löb's theorem

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true", then P is provable in PA. If Prov(P) means that the formula P is provable, we may express this more formally as

If
P A ⊢ P r o v ( P ) → P {\displaystyle PA\,\vdash \,{{\rm {Prov}}(P)\rightarrow P}}
then
P A ⊢ P {\displaystyle PA\,\vdash \,P}

An immediate corollary (the contrapositive) of Löb's theorem is that, if P is not provable in PA, then "if P is provable in PA, then P is true" is not provable in PA. For example, "If 1 + 1 = 3 {\displaystyle 1+1=3} is provable in PA, then 1 + 1 = 3 {\displaystyle 1+1=3} " is not provable in PA.

Löb's theorem is named for Martin Hugo Löb, who formulated it in 1955. It is related to Curry's paradox.

https://en.wikipedia.org/wiki/Löb's theorem
Поиск в словаре
Все словари Английский словарь Англо-арабский словарь Англо-голландский словарь Англо-греческий словарь Англо-испанский словарь Англо-итальянский словарь Англо-немецкий словарь Англо-русский словарь Англо-французский словарь Арабский словарь Голландский словарь Греческий словарь Испанский словарь Итальянский словарь Итальянско-русский словарь Латинско-испанский словарь Латинско-португальский словарь Немецкий словарь Португальский словарь Португальско-русский словарь Русский словарь Французский словарь Французско-русский словарь
Создано ИИ
Английский Русский Испанский Португальский Немецкий Французский Греческий Голландский Итальянский Арабский
Язык интерфейса
Русский English Español Português Deutsch Français Ελληνικά Nederlands Italiano عربي
Контакты
Свяжитесь с нами



Конфиденциальность
Политика конфиденциальности