Kukafika kutsogolo kwa makona kuti: lingaliro, makhalidwe, njira kudziŵa

Triangle ndi mmodzi wa akalumikidzidwa zofunika zojambula woimira atatu mzere zigawo intersecting. chiwerengerochi ankadziwika katswiri wa Egypt, Greece ndi China, zimene zinabweretsa ambiri mitunduyi ndi dongosolo ntchito ndi asayansi, akatswiri ndi okonza kutali.

Mbali yaikulu mbali ya makona ndi:

• pachimake - mfundo ya mphambano ya zigawo.

• Zisangalalo - intersecting mzere zigawo.

Kuchokera pa zigawo izi, zopanga mfundo monga kukafika kutsogolo kwa makona kuderali ake, lolembedwa ndi mabwalo circumscribed. Ku sukulu tikudziwa kuti kukafika kutsogolo kwa makona ndi mawu n'zosangalatsa kumva Muwerenge onse atatu a m'mbali mwake. Pa nthawi yomweyo mitunduyi kupeza phindu ili amadziwika zambiri, malingana deta yaiwisi kuti akatswiri ndi pa nkhani zosiyanasiyana.

1. Njira yosavuta kupeza kukafika kutsogolo kwa makona ntchito ngati pamene mfundo n'zosangalatsa kumva amadziwika onse atatu a m'mbali mwake (×, Y, z), monga Motero:

P = × + Y + z

2. kukafika kutsogolo kwa chinthu cha makona equilateral angapezeke, ngati ife kukumbukira fanizo ili akunjoya Komabe, monga kumathandiza kupeza ngodya onse ndi ofanana. Kudziwa kutalika kwa mbali ya equilateral makona wozungulira kuchita masamu motere:

P = 3x

3. isosceles makona atatu, mosiyana equilateral, mbali ziwiri zokha yemweyo n'zosangalatsa kumva mtengo Koma mu nkhani iyi kukafika kutsogolo mu mawonekedwe onse adzakhala motere:

P = 2X + Y

4. njira zotsatirazi ndi zofunika milandu kumene kudziwika makhalidwe n'zosangalatsa kumva si magulu onse. Mwachitsanzo, ngati kuphunzira ndi deta pa mbali ziwiri, ndi imatchedwanso ngodya therebetween, kukafika kutsogolo kwa makona angapezeke ndi kudziŵa gulu lina ndi mbali kudziwika. Mu nkhani iyi, gulu lina adzapezeka ku njira:

z = 2X + 2y-2xycosβ

Choncho, kukafika kutsogolo kwa makona ndi wofanana:

P = × + Y + 2X + (2y-2xycos β)

5. choncho kumene kutalika poyamba anapatsidwa si mbali oposa mmodzi wa makona ndi odziwika mfundo n'zosangalatsa kumva za kumathandiza kupeza ngodya zabwino zoyandikana thereto, kukafika kutsogolo kwa makona akhoza kuchita masamu pa maziko a Lingaliro Lovomerezeka sine:

P = × + sinβ × / (tchimo (180 ° -β)) + sinγ × / (tchimo (180 ° -γ))

6. milandu komwe ndingapeze wozungulira wa makona ntchito kudziwika magawo bwalo alembedwa mmenemo. chilinganizo Izi ziri zodziwika bwino akadali kwambiri kusukulu:

P = 2S / r Mukhoza (S - malo a bwalo, pamene r Mukhoza - utali wozungulira wa).

Kuchokera pamwamba pa zonse zikuonekeratu kuti mtengo wa kukafika kutsogolo kwa makona ndi angapezeke mu njira zambiri, pa maziko a deta imene kafukufuku wa. Komanso, pali milandu ochepa apadera, kupeza phindu ili. Choncho, kukafika kutsogolo ndi imodzi mwa mfundo zofunika kwambiri ndi makhalidwe a makona bwino-angled.

Monga amadziwika, wotchedwa makona mawonekedwe, mbali ziwiri zomwe kupanga mlingo woyenerera. Kukafika kutsogolo kwa kansalu abwino Uwerenge mawu M'ndandanda kudzera miyendo komanso hypotenuse. Zikatero, ngati kafukufuku deta zodziwika kokha mbali ziwiri, yotsala kuchita masamu ntchito odziwika Pythagorean Lingaliro Lovomerezeka: z = (x2 + y2), ngati odziwika, onse mwendo, kapena × = (z2 - y2), ngati kudziwika hypotenuse ndi mwendo.

Zikatero, ngati ife tikudziwa hypotenuse kutalika ndi moyandikana wina wa pa ngodya zake, ndi mbali zina ziwiri apatsidwa ndi: × = z sinβ, Y = z cosβ. Pankhaniyi, kukafika kutsogolo kwa kansalu bwino ndi wofanana ndi:

P = z (cosβ + sinβ 1)

Komanso, nkhani yapadera ndi mawerengedwe a olondola wozungulira (kapena equilateral) makona, ndiye ngati chithunzi chimene mbali zonse ndipo kumathandiza kupeza ngodya zabwino ndi ofanana. Mawerengedwe a kukafika kutsogolo kwa makona ku mbali kudziwika ndi vuto Komabe, ofufuza zambiri mukudziwa ena deta zina. Choncho, ngati utali wozungulira chodziwika cha bwalo lolembedwa, kukafika kutsogolo kwa kansalu zonse zapatsidwa ndi:

P = 6√3r

Ngati anapatsidwa mtengo wa utali wozungulira bwalo circumscribed, ndi equilateral makona wozungulira opezeka motere:

P = 3√3R

Mitunduyi tiyenera kukumbukira bwino priment kuchita.