A kewaye da alwatika: manufar, halaye, da hanyoyin kayyade

Bamuda shi ne daya daga cikin muhimman lissafi siffofi wakiltar uku intersecting line segments. Wannan adadi da aka sani masanin zamanin d Misira, zamanin tsohuwar Girka da kasar Sin, wanda ya kawo mafi yawan dabarbari da alamu amfani da masana kimiyya, da injiniyoyi, da masu zanen ya zuwa yanzu.

Babban bangaren sassa na alwatika ne:

• ganiya - batun da na rarrabawa da segments.

• Jam'iyyun - intersecting line segments.

Bisa ga wadannan da aka gyara, kirkiro Concepts kamar kewaye da alwatika, ta yanki, rubũtacce da circumscribed da'irori. Daga makaranta muka sani cewa kewaye da alwatika ne na lamba magana da Naira Miliyan Xari da dukan uku daga sãsanninta. A daidai wannan lokaci da dabarbari ga gano wannan darajar da aka sani da yawa, dangane da raw data cewa masu bincike da a wani batu.

1. Mafi sauki hanya zuwa sami kewaye da alwatika aka yi amfani a yanayin saukan idan lamba dabi'u an san ga dukan uku daga sãsanninta (x, y, z), kamar yadda wani sakamako:

P = x + y + z

2. A kewaye da wani equilateral alwatika za a iya samu, idan muka tuna cewa wannan adadi duk jam'iyyun, duk da haka, kamar yadda duk kusassari ne daidai. Sanin tsawon na gefen wani equilateral alwatika kewaye da aka lasafta kamar haka:

P = 3x

3. isosceles alwatika, da bambanci ga equilateral, kawai bangarorin biyu suna da wannan lamba darajar, duk da haka a wannan yanayin da kewaye a general nau'i zai zama kamar haka:

P = 2x + y

4. Wadannan hanyoyin su ne dole a lokuta inda aka sani lamba dabi'u ne ba dukkan jam'iyyun. Alal misali, idan da binciken ne data a kan bangarorin biyu, da kuma aka sanshi kwana therebetween, da kewaye da alwatika za a iya samu ta hanyar kayyade ɓangare na uku da aka fi sani da kwana. A wannan yanayin, da ɓangare na uku zai iya samu daga dabara:

z = 2x + 2y-2xycosβ

Haka kuma, da kewaye da alwatika ne daidai to:

P = x + y + 2x + (2y-2xycos β)

5. A cikin akwati inda da farko aka tsawon ba fiye da daya gefen alwatika da aka sani na lamba dabi'u na biyu kusassari m cikinta, da kewaye da alwatika za a iya lasafta a kan tushen da ba tare da Theorem:

P = x + sinβ x / (zunubi (180 ° -β)) + sinγ x / (zunubi (180 ° -γ))

6. Akwai lokuta inda zan samu kewaye da alwatika amfani da aka sani da sigogi da'irar rubũtacce a cikinta. Wannan dabara ne da aka sani zuwa ga mafi har yanzu a makaranta:

P = 2s / r (S - yanki daga cikin da'irar, alhãli kuwa r - radius).

Daga dukkan sama a fili yake cewa darajar da kewaye na alwatika za a iya samu a hanyoyi masu yawa, a kan tushen da data gudanar da bincike. Bugu da kari, akwai 'yan lokuta na musamman, gano wannan darajar. Saboda haka, kewaye shi ne daya daga cikin mafi muhimmanci dabi'u da kuma halaye na da hakkin-angled alwatika.

Kamar yadda aka sani, don haka ya kira alwatika siffar, bangarorin biyu na wanda ya samar da wata dama kwana. A kewaye da wani hakki Bamuda shi ne Naira Miliyan Xari da wani Tazarar magana ta biyu da kafafu da kuma hypotenuse. A wannan yanayin, idan mai bincike ya sani data kawai a kan bangarorin biyu, da saura za a iya lasafta ta yin amfani da sanannun Pythagorean Theorem: z = (x2 + y2), idan an sani, duka biyu kafa, ko x = (Z2 - y2), idan an sani hypotenuse da kafa.

A wannan yanayin, idan muka san hypotenuse tsawon da m daya daga cikin a cikin sasanninta, da sauran bangarorin biyu ba by: x = z sinβ, y = z cosβ. A wannan yanayin, da kewaye a dama alwatika ne daidai to:

P = z (cosβ + sinβ +1)

Har ila yau, musamman hali ne lissafi na daidai kewaye (ko equilateral) alwatika, cewa shi ne, irin wannan adadi a cikin abin da duk bangarorin da duk kusassari ne daidai. Lissafi na kewaye da alwatika daga sani gefe ne babu matsala, duk da haka, masu bincike sau da yawa san wasu sauran bayanai. Saboda haka, idan aka sani radius daga cikin rubũtacce da'irar, da kewaye a yau da kullum alwatika aka bai da:

P = 6√3r

Idan ba tamanin da radius daga cikin circumscribed da'irar, wani equilateral alwatika kewaye da aka samu kamar haka:

P = 3√3R

Dabarbari bukatar ka tuna to nasarar priment a yi.