To‘rtburchak masalasini vizullashtirish

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To‘rtburchak masalasini vizullashtirish

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Kirish
Hozirgi kunda inson faoliyatida zamonaviy daturlar foydalanishda juda muhim
rol o‘ynamoqda. Sababi: jamiyat taraqqiyotining qaysi jabhasiga nazar solmaylik
o‘zimizga kerakli natijalarni olish uchun, albatta, dasturlarga qilishga majbur bo‘lamiz.
Demak, dasturlashni tashkil qilish axborot almashuv texnologiyasining eng dolzarb hal
qilinadigan muammolaridan biriga aylanib borayotgani davr taqozasidir.
Informatsion texnologiyalarning rivojlanishi va axborot oqimlarining tobora ortib
borishi, ma’lumotlarning tez o‘zgarishi kabi holatlar insoniyatni bu dasturlarni o‘z
vaqtida qayta ishlash choralarining yangi usullarini qidirib topishga undamoqda.
Dasturlarni saqlash, uzatish va qayta ishlash uchun yangi dasturlash tillaridan
foydalanish, so‘ngra undan keng foydalanish bugungi kunda dolzarb bo‘lib qolmokda.
Moliya, ishlab chiqarish, savdo-sotiq va boshqa korxonalar ishlarini zamonaviy
daturlarsiz tasavvur qilib bo‘lmaydi.
Ma’lumki,dasturlash tushunchasi fanga kirib kelgunga qadar, ma’lumotlardan
turli ko‘rinishda foydalanish juda qiyin edi. Dastur tuzuvchilar ma’lumotlarini shunday
tashkil qilar edilarki, u faqat qaralayotgan masala uchungina o‘rinli bo‘lardi. Har bir
yangi masalani hal qilishda ma’lumotlar qaytadan tashkil qilinar va bu hol yaratilgan
dasturlardan foydalanishni qiyinlashtirar edi.
Har qanday axborot tizimining maqsadi real muhit ob’ektlari haqidagi
ma’lumotlarga ishlov berishdan iborat. Keng ma’noda daturlash - bu qandaydir bir
predmet sohasidagi real muhitning aniq ob’ektlari haqidagi ma’lumotlar to‘plamidir.
Predmet sohasi deganda avtomatlashtirilgan boshqarishni tashkil qilish uchun
o‘rganilayotgan real muhitning ma’lum bir qismi tushiniladi. Masalan, korxona, zavod,
ilmiy tekshirish instituti, oliy o‘quv yurti va boshqalar.
Shuni qayd qilish lozimki, dasturni ni yaratishda ikkita muhim shartni hisobga olmoq
zarur:
Birinchidan, ma’lumotlar turi, ko‘rinishi, ularni qo‘llaydigan dasturlash tiliga
bog‘liq bo‘lmasligi lozim, yangi ma’lumotlarni kiritganda yoki ma’lumotlar turini
o‘zgartirganda, programmalarni o‘zgartirish talab etilmasligi lozim.
Bugungi kunda geometrya masalalarini yechuvchi dasturlar ko’p, shunday
dasturlardan biri Geometry daturi hisoblanadi. Quyida Python dasturlash tili yordamida
to‘rtburchak masalasini vizuallashtirishni ko’rib o’tamiz

I. TO‘RTBURCHAKLAR
1.1
Uchtasi bir to‘g‘ri chiziqda yotmaydigan tekislikdagi to'rtta nuqtani ketma-ket
utashtirishdan hosil bo‘lgan geometrik figuraga to‘rthurchak deyiladi.Agar to‘rtburchak
tomoni orqali o‘tgan to‘g‘ri chiziq to‘rtburchak tomonini kessa, bunday to‘rtburchakka
botiq to‘rthurchak deyiladi. Botiq to‘rtburchakni aylanib chiqishda tomonlar turli
tomonda ham (ham o‘ng ham chap tomonda) ko‘rinishi mumkin
Agar tcfrtburchak tomoni orqali o‘tgan 10‘g‘ri chiziq to'rtburchak tomonini kesmasa,
bundayto‘rtburchakka qavariq to'rtburchak deyiladi. Qavariq lo‘rtburchakni aylanib
chiqishda tomonlarfaqat bir tomonda (yoki o‘ng yoki chap tomonda) ko‘rinishi mumkin
(16.24. l-a,rasm).Bizni ko‘proq faqat qavariq to‘rtburchak qiziqtirgani bois, shunga oid
masalalar bilan shug‘ullanamiz. To‘rtburchakning uchlarini lotincha katta harflar bilan
belgilanadi. Uning tomonlarini esa uchlarini ifadalovchi katta harflar yoki lotincha
kichik harflar bilan belgilanadi.
To‘rtburchakning bitta uchida tutashuvchi tomonlarga qo'shni tomonlar
deyiladi.Umumiy uchga cga bo‘lmagan tomonlarga qarama-qarshi tomonlar deyiladi.
Umumiy tomonga ega bo‘lgan burchaklarga qo'shni burchaklar deyiladi. Umumiy
tomonga ega bo‘lgan burchaklarga qarama-qarshi burchaklar deyiladi
To‘rtburchak tomonlar uzunliklari yig‘indisiga to‘rtburchak perimetri deyiladi. Umumiy
hc to‘rtburchak perimetri quyidagi ko‘rinishda bo‘ladi:
To'rtburchakning qarama-qarshi uchlarini tutashtiruvchi kesmaga uning diagonali
dcyiladi.To‘rtburchak ikkita diagonalga ega boTib, umumiy holda berilgan
to‘rtburchaklar diagonallari turlicha uzunlikka cga bo‘ladi.

Agar to‘rtburchakning tomonlari va ixtiyoriy ikkita qo‘shni burchaklari malum bolsa,
uning diagonallarini aniqlash mumkin
Umumiy holda berilgan to‘rtburchakning tomonlar o‘rtalarini tutashtiruvchi
kesmalardan iborat figura pallelogramni hosil qiladi. Bu parallelogram tomonlari
to‘rtburchak diagonallariga parallel bo‘lib, diagonal uzunliklarining yarmiga teng
bo‘ladi, yuzasi ham berilgan parallelogram yuzasining yarmiga teng bo'ladi.
To‘rtbo‘rchak diagonallari va diagonallar orasidagi burchak malum bo’lsa, to‘rtburchak
vuzasini aniqlash mumkin.
To‘rtburchakka ichki va tashqi chizilgan aylana.
To‘rtburchak uchlariga urinadigan aylanaga to‘rtburchakka tashqi chizilgan aylana
deyiladi. Umumiy holda berilgan hamma to‘rtburchaklarga ham tashqi aylana chizib
bolavermaydi.Buning uchun ma’lum bir shartlar bajarilish kerak. Agar to‘rtburchakning
qarama-qarshi burchaklari yig’indisi 180° ga teng bo’lsa, bundagi to‘rtburchakka tashqi
aylana chizish mumkin.
Paralalegram
Qarama-qarshi tomonlari teng va parallel bo'lgan to‘rtburchakka parallelogram deyiladi
Parallelogramning uchlarini lotincha katta harflar bilan, tomonlarini esauchlarini
ifadalovchi katta harflar yoki lotincha kichik harflar bilan belgilanadi.

Parallelogramning qarama-qarshi uchidagi burchaklari o'zaro teng bo'ladi.

Parallelogramning qo‘shni uchidagi burchaklari yig‘indisi 180°ga teng bo'ladi.
Tomonlari a va b bo‘lgan parallelogramning perimetri
quyidagicha bo'ladi:

Qarama-qarshi uchlarini tutashtiruvchi kesmaga uning diagonali deyiladi.
Parallelogramlar ikkita diagonalga ega bo'lib umumiy holda bu diagonallar o‘zaro teng
emas.
Parllelogramning a va b tomonlari orasidagi o‘tkir burchagi α ekani ma'lum bo‘lsa, u
holda parallelogramning kichik diagonali d
1 va katta diagonali d
2 kosinuslar
teoremasidan hisoblab topiladi
To‘g‘ri to‘rtburchak.
Hamma burchaklari to‘g‘ri (90°) bo‘lgan to‘rtburchakka to‘g‘ri to'rtburchakdeyiladi.
Tomonlari a va b boTgan to‘g‘ri to'rtburakning perimetri
quyidagicha bo’ladi

To‘g‘ri to‘rtburchakning ikkita diagonali ham o‘zaro tengdir. Diagonallar kesishish
nuqtasida teng ikkiga bo‘linadi.To‘g‘ri to'rtburchak diagonali va tomonlari orasida
quyidagi bog‘lanish mavjud .

To‘g‘ri to'rtburchak tomonlari ma'lum bo'lsa, yuzasini quyidagicha aniqlash mumkin
bo’ladi .

Agar to‘g‘ri to‘rtburchakning diagonali va diagonallar orasidagi burchak berilgan
bo‘lsa, uning yuzasi quiydagicha bo'ladi .

ABCD to‘g‘ri to‘rtburchakning ichida olingan ixtiyony P nuqtadan to‘rtburchakning
uchlarigacha masofalar quyidagi formula yordamida bog'lanadi

Romb

Kvadrat.
To'rtta tomoni ham to'rtta burchagi ham o'zaro teng bo’lgan parallelogramga kvadrat
deyiladi.
Trapetsiya

Traspetsdiyaga ichki va tashqi chizilgan aylana
DASTUR KODI
import turtle
a=turtle.Turtle()
a.forward(200)
a.left(90)
a.forward(100)
a.left(90)
a.forward(200)
a.left(90)
a.forward(100)
a.left(90)
def plot_triangle(A, B, C, color):

x1, y1 = A[0], A[1]
x2, y2 = B[0], B[1]
x3, y3 = C[0], C[1]

$import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (20, 10) plt.style.use('ggplot') fig = plt.plot([x1, x2, x3, x1], [y1, y2, y3, y1], color = color, linewidth = 2) plt.scatter([x1, x2, x3, x1], [y1, y2, y3, y1], color = 'red', linewidth = 3) plt.fill([x1, x2, x3, x1], [y1, y2, y3, y1], color = color, alpha = 0.3) plt.xticks(fontsize = 14) plt.yticks(fontsize = 14) plt.savefig('triangle.png') return fig def find_quadrilateral_area(A, B, C, D): x1, y1 = A[0], A[1] x2, y2 = B[0], B[1] x3, y3 = C[0], C[1] x4, y4 = D[0], D[1] area = (x1*y2 + x2*y3 + x3*y4 + x4*y1) - (y1*x2 + y2*x3 + y3*x4 + y4*x1) area = abs(area * 0.5) return area def check_quadrilateral_collinearity(A, B, C, D): area = find_quadrilateral_area(A, B, C, D) if area == 0.0: message = str('Given vertices {}, {}, {}, {} are collinear'.format(A, B, C, D)) else: message = str('Given vertices {}, {}, {}, {} are not collinear'.format(A, B, C, D)) return message def plot_quadrilateral(A, B, C, D, color): x1, y1 = A[0], A[1] x2, y2 = B[0], B[1] x3, y3 = C[0], C[1] x4, y4 = D[0], D[1] import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (20, 10) plt.style.use('ggplot')$ $fig = plt.plot([x1, x2, x3, x4, x1], [y1, y2, y3, y4, y1], color = color, linewidth = 2) plt.scatter([x1, x2, x3, x4, x1], [y1, y2, y3, y4, y1], color = 'b', linewidth = 3) plt.fill([x1, x2, x3, x4, x1], [y1, y2, y3, y4, y1], color = color, alpha = 0.3) plt.title('Quadrilateral for the given vertices A = {}, B = {}, C = {}, D = {}'.format(A, B, C, D), fontsize = 18) plt.xticks(fontsize = 14) plt.yticks(fontsize = 14) return fig def find_triangle_coordinates(P, Q, R): p1, p2 = P[0], P[1] q1, q2 = Q[0], Q[1] r1, r2 = R[0], R[1] A = [] B = [] C = [] a1 = p1 + r1 - q1 a2 = p2 + r2 - q2 b1 = q1 + p1 - r1 b2 = q2 + p2 - r2 c1 = r1 + q1 - p1 c2 = r2 + q2 - p2 A.append(a1) A.append(a2) B.append(b1) B.append(b2) C.append(c1) C.append(c2) return A, B, C def find_triangle_area(A, B, C): x1, y1 = A[0], A[1] x2, y2 = B[0], B[1] x3, y3 = C[0], C[1] area = (x1*y2 + x2*y3 + x3*y1) - (y1*x2 + y2*x3 + y3*x1) area = abs(area * 0.5)$ $return area def check_triangle_collinearity(A, B, C): area = find_triangle_area(A, B, C) if area == 0.0: message = str('Given vertices {}, {}, {} are collinear'.format(A, B, C)) else: message = str('Given vertices {}, {}, {} are not collinear'.format(A, B, C)) return message def compare_triangles(triangle_area, midpoint_area): message = str('The area of triangle is {} times larger than the midpoint triangle'.format(int(triangle_area/midpoint_area))) return message def plot_triangle(A, B, C, color): x1, y1 = A[0], A[1] x2, y2 = B[0], B[1] x3, y3 = C[0], C[1] import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (20, 10) plt.style.use('ggplot') fig = plt.plot([x1, x2, x3, x1], [y1, y2, y3, y1], color = color, linewidth = 2) plt.scatter([x1, x2, x3, x1], [y1, y2, y3, y1], color = 'red', linewidth = 3) plt.fill([x1, x2, x3, x1], [y1, y2, y3, y1], color = color, alpha = 0.3) plt.xticks(fontsize = 14) plt.yticks(fontsize = 14) plt.savefig('triangle.png') return fig def find_quadrilateral_area(A, B, C, D): x1, y1 = A[0], A[1] x2, y2 = B[0], B[1] x3, y3 = C[0], C[1] x4, y4 = D[0], D[1] area = (x1*y2 + x2*y3 + x3*y4 + x4*y1) - (y1*x2 + y2*x3 + y3*x4 + y4*x1) area = abs(area * 0.5)$ $return area def check_quadrilateral_collinearity(A, B, C, D): area = find_quadrilateral_area(A, B, C, D) if area == 0.0: message = str('Given vertices {}, {}, {}, {} are collinear'.format(A, B, C, D)) else: message = str('Given vertices {}, {}, {}, {} are not collinear'.format(A, B, C, D)) return message def plot_quadrilateral(A, B, C, D, color): x1, y1 = A[0], A[1] x2, y2 = B[0], B[1] x3, y3 = C[0], C[1] x4, y4 = D[0], D[1] import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (20, 10) plt.style.use('ggplot') fig = plt.plot([x1, x2, x3, x4, x1], [y1, y2, y3, y4, y1], color = color, linewidth = 2) plt.scatter([x1, x2, x3, x4, x1], [y1, y2, y3, y4, y1], color = 'b', linewidth = 3) plt.fill([x1, x2, x3, x4, x1], [y1, y2, y3, y4, y1], color = color, alpha = 0.3) plt.title('Quadrilateral for the given vertices A = {}, B = {}, C = {}, D = {}'.format(A, B, C, D), fontsize = 18) plt.xticks(fontsize = 14) plt.yticks(fontsize = 14) return fig # Triangle from termcolor import colored as cl import matplotlib.pyplot as plt Pt, Qt, Rt = [12, 6], [11,4], [8,4] At, Bt, Ct = find_triangle_coordinates([12, 6], [11,4], [8,4]) area_t = find_triangle_area(At, Bt, Ct) area_mt = find_triangle_area(Pt, Qt, Rt) ct = compare_triangles(area_t, area_mt) collinearity_t = check_triangle_collinearity(At, Bt, Ct) print(cl('----------------------------------------------------------------------', attrs = ['bold']))$ $print(cl('The given midpoints are\n P = {}\n Q = {}\n R = {}'.format(Pt, Qt, Rt), attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl('The coordinates of triangle are\n A = {}\n B = {}\n C = {}'.format(At, Bt, Ct), attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl('The area of the triangle is {} sq.units'.format(area_t), attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl('The area of midpoint triangle is {} sq.units'.format(area_mt), attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl(collinearity_t, attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl(ct, attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) plot_triangle(At, Bt, Ct, 'black') plot_triangle(Pt, Qt, Rt, 'b') # Quadrilateral Aq, Bq, Cq, Dq = [-4,-2], [-3,-5], [3,-2], [2,3] area_q = find_quadrilateral_area(Aq, Bq, Cq, Dq) collinearity_q = check_quadrilateral_collinearity(Aq, Bq, Cq, Dq) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) print(cl('The coordinates of quadrilateral are A = {}, B = {}, C = {}, D = {}'.format(Aq, Bq, Cq, Dq), attrs = ['bold'])) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) print(cl('The area of quadrilateral is {} sq.units'.format(area_q), attrs = ['bold'])) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) print(cl(collinearity_q, attrs = ['bold'])) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) plot_quadrilateral(Aq, Bq, Cq, Dq, 'r') print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl('The given midpoints are\n P = {}\n Q = {}\n R = {}'.format(Pt, Qt, Rt), attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl('The coordinates of triangle are\n A = {}\n B = {}\n C = {}'.format(At, Bt, Ct), attrs = ['bold']))$ $print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl('The area of the triangle is {} sq.units'.format(area_t), attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl('The area of midpoint triangle is {} sq.units'.format(area_mt), attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl(collinearity_t, attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) print(cl(ct, attrs = ['bold'])) print(cl('----------------------------------------------------------------------', attrs = ['bold'])) plot_triangle(At, Bt, Ct, 'black') plot_triangle(Pt, Qt, Rt, 'b') # Quadrilateral Aq, Bq, Cq, Dq = [-4,-2], [-3,-5], [3,-2], [2,3] area_q = find_quadrilateral_area(Aq, Bq, Cq, Dq) collinearity_q = check_quadrilateral_collinearity(Aq, Bq, Cq, Dq) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) print(cl('The coordinates of quadrilateral are A = {}, B = {}, C = {}, D = {}'.format(Aq, Bq, Cq, Dq), attrs = ['bold'])) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) print(cl('The area of quadrilateral is {} sq.units'.format(area_q), attrs = ['bold'])) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) print(cl(collinearity_q, attrs = ['bold'])) print(cl('------------------------------------------------------------------------------------------', attrs = ['bold'])) plot_quadrilateral(Aq, Bq, Cq, Dq, 'r')$

XULOSA
Ushbu kurs ishi loyihasi pyutonda amalga oshiriladi. Loyiha geometrik masalarni
natijasini olish jarayonini avtomatlashtirishga mo'ljallangan.
Ushbu dastur ta‘limning turli soxalarida yengilliklar olib keladi. O‘qituvchilarga
qo‘shimcha qulayliklar olib keladi hamda o‘quvchilarning IT soxasiga bo‘lgan
qiziqishini ortiradi IT soxasi hozirgi kundagi zamonaviy soxa hisoblanadi.
Ushbu kurs ishida biz to‘rtburchaklar haqida umumiy tushunchalarni keltirdik ,
to‘rtburchak masalasini vizallashtirish dasturining umumiy algoritimi hamda so‘ngida
pythonda tuzilgan dasturini ham keltirib o‘tdik.
Dasturimizni ishlash prinspi to‘rtburchak masalasini vizuallashtirishda har xil turdagi
to‘rtburchalarning chizmasi hamda ishlanish yo‘lini ko‘rsatadi.

Foydalanilgan adabiyotlar ro'yxati
1. Бекаревич Ю. Microsoft Access 2003. БХВ-Петербург, 2004
2. Владимиров К.К. Основы создания реляционных СУБД. БХВ-Петербург,
2004
3. Дорогин П.З. Разработка и проектирование баз данных. БХВ-Петербург,
2001
4. Захарченко П.Ф. Поектирование и программирование запросов в Microsoft
Access 2003. ЮСпро, 2000
5. www.sei.cmu.edu Software Engineering .
6. http: //www. intuit. r u.

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