Tsawo

Tsawon ma'auni ne na nesa. A cikin Tsarin Ƙididdigar Duniya, tsawon adadi ne tare da nisa mai girman. A mafi yawan tsarin aunawa an zaɓi tushe na tsawon, daga abin da aka samo duk sauran raka'a. A cikin tsarin Ƙungiyoyin Duniya (SI), ma'auni na tushe don tsawon shine mita.

Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in.

Ana amfani da kalmomi daban-daban don tsawo wani abu mai tsawo, kuma waɗannan sun haɗa da tsawo, wanda shine tsawon tsaye ko tsayin tsaye, faɗin, faɗin da zurfin. Ana amfani da Tsawon lokacin da akwai tushe wanda za'a iya ɗaukar ma'auni na tsaye. 'faɗin' da faɗin yawanci suna nufin ɗan gajeren girma fiye da tsawon. Ana amfani da zurfi don auna ma'auni na uku.^[1]

Tsawon shine ma'auni na girman sararin samaniya guda ɗaya, Yankin da yanki shine ma'ana na ma'aunin ma'aoni biyu (tsawon murabba'i) kuma girma shine ma'ƙarar ma'auri uku (tsawon cubed).

Tarihi

Aunawa ya kasance mai mahimmanci tun lokacin da mutane suka zauna daga salon rayuwa na nomadic kuma suka fara amfani da kayan gini, suna zaune a ƙasa da kasuwanci tare da makwabta. Yayinda cinikayya tsakanin wurare daban-daban ke ƙaruwa, buƙatar daidaitattun raka'a na tsawon ya ƙaru. Kuma daga baya, yayin da al'umma ta zama mafi dacewa da fasaha, ana buƙatar daidaito mafi girma na ma'auni a cikin fannoni daban-daban, daga micro-electronics zuwa kewayon duniya.

A karkashin ma'auni na musamman na Einstein, tsawon ba za a iya tunanin shi a matsayin mai ɗorewa a duk tsarin tunani ba. Don haka mai mulki wanda ke da tsawon mita ɗaya a cikin firam ɗaya na tunani ba zai zama tsawon mita ɗaya ba a cikin firamin da ke motsawa dangane da firam na farko. Wannan yana nufin tsawon wani abu ya bambanta dangane da saurin mai kallo.^[2]

Amfani da lissafi

Tsarin lissafi na Euclid

A cikin lissafin Euclidean, ana auna tsawon tare da layi madaidaiciya layi dai idan an ƙayyade ba kuma yana nufin ɓangarori a kansu. Ka'idar Pythagoras da ke danganta tsawon bangarorin triangle na dama yana daya daga cikin aikace-aikace da yawa a cikin lissafin Euclidean. Hakanan ana iya auna tsawon tare da wasu nau'ikan ƙwaƙwalwa kuma ana kiransa tsawon arc.

A cikin triangle, tsawo tsawo, ɓangaren layin da aka zana daga maɓallin da ke tsaye zuwa gefen da ba ya wucewa ta maɓallin (wanda ake kira tushe na triangle), ana kiransa tsawo na triangle.

Yankin rectangle an bayyana shi don zama tsawon × faɗin rectangle. Idan an tsaya wani rectangle mai tsawo a kan gajeren gefensa to ana iya bayyana yankin sa a matsayin tsayinsa × faɗin.

Girman akwati mai tsayi na rectangular (ƙarar allon itace) ana bayyana shi sau da yawa a matsayin tsawon × tsawo × zurfin.

Yankin polygon shine jimlar tsawon bangarorin sa.

Yankin da ke kewaye da faifai zagaye shine tsawon iyaka (da'irar) na wannan faifai.

Sauran lissafi

A wasu lissafi, ana iya auna tsawon tare da yiwuwar hanyoyin da aka yi amfani da su, wanda ake kira geodesics. Geometry na Riemannian da aka yi amfani da shi a cikin ma'auni na gaba ɗaya misali ne na irin wannan lissafi. A cikin lissafin lissafi, ana auna tsawon tare da manyan da'irori a kan da'irar kuma nisan tsakanin maki biyu a kan da ke cikin shi shine mafi ƙanƙanta daga cikin tsayi biyu a kan babban da'irar, wanda jirgin ya ƙayyade ta hanyar maki biyu da tsakiyar da'irar.

Ka'idar hoto

A cikin jadawalin da ba a a auna shi ba, tsawon sake zagayowar, hanya, ko tafiya shine yawan gefuna da yake amfani da su.^[3] A cikin jadawalin da aka auna yana iya zama jimlar nauyin gefuna da yake amfani da su.^[4]

Ana amfani da tsawon don bayyana hanya mafi ƙanƙanta, girth (tsawon zagaye mafi ƙaranci), da kuma hanya mafi tsawo tsakanin maɓuɓɓuka biyu a cikin jadawalin.

Ka'idar auna

A cikin ka'idar ma'auni, tsawon sau da yawa ana amfani da shi ga saiti na gaba ɗaya na

R

n

{\displaystyle \mathbb {R} ^{n}}

ta hanyar ma'auni na Lebesgue. A cikin yanayin guda ɗaya, an bayyana ma'auni na waje na Lebesgue na saiti dangane da tsawon lokacin budewa. A takaice dai, an fara bayyana tsawon lokacin budewa kamar haka

ℓ ({x \in ℝ ∣ a < x < b}) = b - a .

don haka ma'auni na waje na Lebesgue

μ

Sanya

(E)

{\displaystyle \mu ^{*} (E) }

na gaba ɗaya

E

{\displaystyle E}

ana iya bayyana shi kamar yadda ^[5]

μ^{*} (E) = inf {\sum_{k} ℓ (I_{k}) : I_{k} is a sequence of open intervals such that E \subseteq ⋃_{k} I_{k}} .

Kimiyya ta kwamfuta

A cikin kimiyyar kwamfuta, tsawon igiya shine yawan Haruffa da suka hada da igiya. Misali, bit string

10010100001

{\displaystyle {\texttt {10010100001}}}

yana da tsawon 11.

Yawancin harsunan shirye-shirye suna da nau'in bayanan kirtani tare da hanyar don tsawon don dawo da tsawon kirtani.

String s = "Hello, world!";
int len = s.length(); // len = 13

"tsawon" tsarin bayanai na tsari, kamar jerin abubuwa, ana iya bayyana su azaman yawan abubuwan da ke ciki.

import java.util.List;

int[] a = {1, 2, 3, 4, 5};
int len = a.length; // len = 5

List<Integer> list = List.of(1, 2, 3, 4, 5, 6, 7, 8);
int len = list.size(); // len = 8

Rukunin

A cikin kimiyyar jiki da injiniya, lokacin da mutum ke magana game da raka'a na tsawon, tsawon kalma daidai yake da nesa. Akwai raka'a da yawa da ake amfani da su don auna tsawon. A tarihi, ana iya samun raka'a na tsawon sassan jikin mutum, nisan da aka yi tafiya a matakai da yawa, nisan tsakanin alamomi ko wurare a Duniya, ko kuma a kan tsawon wasu abubuwa na yau da kullun.

A cikin Tsarin Ma’auni na Ƙasa da Ƙasa (SI), ma’aunin asali na tsawo shi ne mita (metre), wanda ake rubutawa da alamar m. Yanzu ana bayyana mita ne ta amfani da saurin haske, wanda yake kusan mita miliyan 300 a cikin daƙiƙa guda.

Sauran ma’aunan tsawo da ake samu daga mita kuma ana amfani da su sosai sun hada:da:millimita,sentimental,kilomita

A cikin ma’aunin Amurka (U.S. customary units), ko kuma English/Imperial system, ma’aunan tsawo da ake amfani da su sun haɗa da:inci(inch-in),kafa(foot-fit),yadi(yard-yd),mil(mile-mi).

Akwai kuma wani ma’aunin tsawo da ake amfani da shi wajen kewayawa ko zirga-zirgar jiragen ruwa, wanda ake kira mil ɗin teku (nautical mile – nmi).

1 mile = 1.609344 km

Wato, mil 1 daidai yake da kilomita 1.609344

Rukunin da aka yi amfani da su don nuna nisa a cikin sararin samaniya, kamar yadda yake a cikin ilimin taurari, sun fi tsayi fiye da waɗanda aka saba amfani da su a Duniya (mita ko kilomita) kuma sun haɗa da rukunin taurari (au), shekara-haske, da parsec (pc).

Rukunin da aka yi amfani da su don nuna nisan sub-atomic, kamar yadda yake a kimiyyar nukiliya, sun fi karami fiye da millimetre. Misalan sun hada da fermi (fm).

Dubi kuma

Tsawon bakan gizo
Rukunin ban dariya na tsawon
Ma'auni na tsawon
Tsarin ma'auni
Ƙididdigar ma'auni
Dokokin girman (tsawon)
Tsawon ma'ana

Bayanan da aka ambata

↑ "Measurement: Length, width, height, depth". Think Math!. Archived from the original on 24 February 2020. Retrieved 15 March 2020.
↑ "Time Dilation and Length Contraction". Student Academic Success (in Turanci). Retrieved 2026-09-16.
↑ Caldwell, Chris K. (1995). "Graph Theory Glossary". Archived from the original on 2022-10-22. Retrieved 2020-03-18.
↑ Cheung, Shun Yan. "Weighted graphs and path length". Archived from the original on 2020-01-09. Retrieved 2020-03-18.
↑ Le, Dung. "Lebesgue Measure" (PDF). Archived (PDF) from the original on 2010-11-30.

[1] "Measurement: Length, width, height, depth". Think Math!. Archived from the original on 24 February 2020. Retrieved 15 March 2020.

[2] "Time Dilation and Length Contraction". Student Academic Success (in Turanci). Retrieved 2026-09-16.

[3] Caldwell, Chris K. (1995). "Graph Theory Glossary". Archived from the original on 2022-10-22. Retrieved 2020-03-18.

[4] Cheung, Shun Yan. "Weighted graphs and path length". Archived from the original on 2020-01-09. Retrieved 2020-03-18.

[5] Le, Dung. "Lebesgue Measure" (PDF). Archived (PDF) from the original on 2010-11-30.

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