Samarqand davlat universiteti raqamli texnologiyalar fakulteti dasturiy injiniring yo
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Nazorat ishi uchun namunalarUchburchakning uchlari A,B,C nuqtalar koordinatalari bilan berilgan. Topish kerak: 1) ABC tomonlarining tenglamalarini va uzunliklarini; 2) AB va AC tomonlar orasidagi burchak bissektirsa tenglamasini 3) AD balandlik tenglamasi va uzunligini 4) AE mediana tenglamsini 5) ABC ni ichki burchaklarini 6) ABC ning yuzini № 1
2 3
4 5
6 A (2;2), B (3;3), C (-4;4) A (1;3), B (2;1), C (2;-1) A (1; -1), B (6;1), C (4;3) A (-1;1), B (6;-1), C (4;-3) A (2;-1), B (6;-1), C (-4;3) A (1;-6), B (2;1), C (0;1) № 7 8 9
10 11
12 A (2;1), B (-2;1), C (2;0) A (1;2), B (-1;-2), C (0;-3), A (1;-2), B (-1;-1), C (15;-1) A (2;2), B (-2;-2), C (0;2), A (3;-1), B (1;-2), C (3;-3) A (1;5), B (2;-2), C (-4;2) № 13 14 15
16 17
18 A (1;4), B (2;3), C (-4;2) A (1;1), B (2;2), C (3;-3) A (2;2), B (1;1), C (-1;5) A (-4;4), B (3;3), C (0;1) A (1;2), B (2;1), C (2;0) A (3;3), B (-3;3), C (0;6) № 19 20 21
22 23
24 A (2;2), B (4;1), C (2;0) A (2;1), B (3;-3), C (1;4) A (1;3), B (4;1), C (0;5) A (1;4), B (1;1), C (2;0) A (-4;3), B (3;2), C (3;0) A (1;1), B (-1;2), C (4;3) № 25 26 27
28 29
30 A (-6;7), B (2;1), C (0;-1) A (4;3), B (0;4), C (1;1) A (4;1), B (1;-5), C (2;2) A (6;-2), B (1;0), C (3;0) A (2;-5), B (0;3), C (1;1) A (3;-3), B (-1;0), C (2;1) Koordi
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na > with(geometry); > point(A,3,1 ), point(B, 1, -2); > l1 := line(AB, [A, B]); print(`output redirected...`); # input placeholder AB > Equation(AB, [x, y]); print(`output redirected...`); # input placeholder -x + y = 0 > with(geometry); > point(A, 2, 2), point(C, 3, -3); > l2 := line(AC, [A, C]); print(`output redirected...`); # input placeholder AC > Equation(AC, [x, z]); print(`output redirected...`); # input placeholder 16 - 2 x - 6 z = 0 > with(geometry); > point(B, 1 -2) (BC, [B, C]); print(`output redirected...`); # input placeholder BC > Equation(BC, [y, z]); print(`output redirected...`); # input placeholder 24 - y - 7 z = 0 > with(geometry); > triangle(ABC, [point(A3, -1), point(B, 1, -2), point(C, -3,-3)]); > distance(A, B); distance(A, C); distance(B, C); print(`output redirected...`); # input placeholder (1/2) 2
(1/2) 40
(1/2) 50
> sides(ABC); print(`output redirected...`); # input placeholder [ (1/2) (1/2) (1/2)] [2 , 50 , 40 ] > with(geometry); > EnvHorizontalName := 'x'; _EnvVerticalName := 'y'; > line(AB, -X-Y = 0), line(AC, 16-2*x-6*Z = 0); %; Warning, computation interrupted > hi := FindAngle(AB, AC); print(`output redirected...`); # input placeholder /1\ arctan|-| \2/ > hi := evalf(hi); print(`output redirected...`); # input placeholder 0.4636476090 > with(geometry); > triangle(ABC, [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]); > altitude(hA1, A, ABC); print(`output redirected...`); # input placeholder hA1 > form(hA1); print(`output redirected...`); # input placeholder line2d
> detail(hA1); print(`output redirected...`); # input placeholder assume that the names of the horizontal and vertical axes are _x and _y, respectively GeometryDetail(["name of the object", hA1], ["form of the object", line2d], ["equation of the line", 12 - 7 _x + _y = 0]) > with(geometry); > assume(m <> 0); > line(BC, 24-y-7*Z = 0, [x, y]); distance(A, BC); print(`output redirected...`); # input placeholder |-22 + 7 Z| > with(geometry); > triangle(ABC, [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]); > median(mA, A, ABC); print(`output redirected...`); # input placeholder mA > form(mA); print(`output redirected...`); # input placeholder line2d
> detail(mA); print(`output redirected...`); # input placeholder assume that the names of the horizontal and vertical axes are _x and _y, respectively /
GeometryDetail|["name of the object", mA], ["form of the object", line2d], \
["equation of the line", 8 - - _x - - _y = 0]| [ 2 2 ]/
> median(mA, A, ABC, E); print(`output redirected...`); # input placeholder mA > form(mA); print(`output redirected...`); # input placeholder segment2d > coordinates(E); print(`output redirected...`); # input placeholder [-1 7] [--, -]
[2 2] > detail(mA); print(`output redirected...`); # input placeholder /
GeometryDetail|["name of the object", mA], ["form of the object", segment2d], \
["the two ends of the segment", [[2, 2], [--, -]]]| [ [ [2 2]]]/ > with(geometry); > s := [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]; print(`output redirected...`); # input placeholder [A, B, C] > centroid(G, s); print(`output redirected...`); # input placeholder G > form(G); print(`output redirected...`); # input placeholder point2d
> coordinates(G); print(`output redirected...`); # input placeholder [1 ] [-, 3]
[3 ] > detail(G); print(`output redirected...`); # input placeholder /
GeometryDetail|["name of the object", G], ["form of the object", point2d], \
["coordinates of the point", [-, 3]]| [ [3 ]]/
> with(geometry); > triangle(T, [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]); > medial(mT, T); print(`output redirected...`); # input placeholder mT > detail(mT); print(`output redirected...`); # input placeholder /
GeometryDetail|["name of the object", mT], ["form of the object", triangle2d], \
[ [[5 5] [-1 7]]]\ ["the three vertices", [[-, -], [-1, 3], [--, -]]]| [ [[2 2] [2 2]]]/ > with(geometry); > triangle(ABC, [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]); > bisector(bA, A, ABC); print(`output redirected...`); # input placeholder bA > Equation(bA, [x, y]); print(`output redirected...`); # input placeholder / (1/2) (1/2)\ / (1/2) (1/2)\ (1/2) \-2 2 - 40 / x + \40 - 6 2 / y + 16 2 = 0 > detail(bA); print(`output redirected...`); # input placeholder /
GeometryDetail\["name of the object", bA], ["form of the object", line2d], [ ["equation of the line", / (1/2) (1/2)\ / (1/2) (1/2)\ (1/2) ]\ \-2 2 - 40 / x + \40 - 6 2 / y + 16 2 = 0]/ > with(geometry); > triangle(ABC, [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]); > ExternalBisector(bA, A, ABC); print(`output redirected...`); # input placeholder bA > Equation(bA, [x, y]); print(`output redirected...`); # input placeholder / (1/2) (1/2)\ / (1/2) (1/2)\ (1/2) (1/2) \40 - 6 2 / x + \2 2 + 40 / y + 8 2 - 4 40 = 0 > detail(bA); print(`output redirected...`); # input placeholder /
GeometryDetail\["name of the object", bA], ["form of the object", line2d], [ ["equation of the line", / (1/2) (1/2)\ / (1/2) (1/2)\ (1/2) (1/2) ]\ \40 - 6 2 / x + \2 2 + 40 / y + 8 2 - 4 40 = 0]/ > bisector(ibA, A, ABC); > ArePerendicular(bA, ibA); print(`output redirected...`); # input placeholder ArePerendicular(bA, ibA) > restart; > with(geometry); > triangle(ABC, [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]); > bisector(bA, A, ABC, N); print(`output redirected...`); # input placeholder bA > form(bA); print(`output redirected...`); # input placeholder segment2d > OnSegment(N, B, C, sqrt(212/(61.))); print(`output redirected...`); # input placeholder N > coordinates(N); print(`output redirected...`); # input placeholder [-1.556075082, 3.650867870] > detail(bA); print(`output redirected...`); # input placeholder GeometryDetail(["name of the object", bA], ["form of the object", segment2d],
> with(geometry); > triangle(ABC, [point(A, 2, 2), point(B, 3, 3), point(C, -4, 4)]); line(BC, [B, C]); print(`output redirected...`); # input placeholder BC > ParallelLine(lA, A, BC); print(`output redirected...`); # input placeholder lA > Equation(lA, [x, y]); print(`output redirected...`); # input placeholder 16 - x - 7 y = 0 > detail(lA); print(`output redirected...`); # input placeholder GeometryDetail(["name of the object", lA], ["form of the object", line2d],
>
> >
> XULOSA:
BIZ MEPLE dasturi orqali uchburchakning tomonlarini tenglamalarini tomonlari orqali bessektritsa tenglamalarini medina tenglamalarrini yuzini topishni organdik. Foydalanilgan adabiyotlar 1. Матросов А. Решение задач математики и механики в среде Maple 6. СПб.: Питер, 2000. 2. В.З. АЛАДЬЕВ. Основы программирования в Maple. Таллинн, 2006. 3. Основы использования математического пакета Maple в моделировании: Учебное пособие / Международный институт компьютерных технологий. Липецк, 2006. 119с. 4. Дьяконов В. Maple 6. Учебный курс СПб.: Питер, 2001. 5. Аладьев В.З., Лиопо В.А., Никитин А.В. Математический пакет Maple в физическом моделировании.- Гродно: Гродненский госу-дарственный университет им. Янки Купалы, 2002, 416 с. 6. O’runbayev E., Murodov F. Kompyuter algebrasi tizimlarining amaliy tadbiqlari. –SamDU nashri – Samarqand, 2003, 96 s. 7. Аладьев В.З., Богдявичюс М.А. Решение физико-технических и математических задач с пакетом Maple V.- Вильнюс: Изд-во Техника, 1999, 686 c., ISBN 9986-05-398-6. 8. Аладьев В.З., Богдявичюс М.А. Maple 6: Решение математичес-ких, статистических и инженерно-физических задач.- Москва: Лаборатория Базовых Знаний, 2001, 850 с. + CD-ROM, ISBN 5-93308-085-X. 9. Математика на компьютере: Maple 8. — М.: СОЛОН-Пресс, 2003.176 с: Yüklə 182,49 Kb. Dostları ilə paylaş:
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