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Ɍɟɩɟɪɶ ɹ ɩɨɡɧɚɤɨɦɥɸ ɜɚɫ ɫ ɢɧɬɟɪɟɫɧɵɦ ɩɨɧɹɬɢɟɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ –
ɩɫɟɜɞɨɤɨɞ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɦɵ ɩɢɲɟɦ ɩɪɨɝɪɚɦɦɭ ɤɚɤ ɛɵ ɩɨ-ɪɭɫɫɤɢ, ɧɨ
ɢɦɟɹ ɜ ɝɨɥɨɜɟ, ɱɬɨ ɱɭɬɶ ɩɨɡɠɟ ɜɫɺ ɷɬɨ ɛɭɞɟɬ ɩɟɪɟɜɟɞɟɧɨ ɫ ɪɭɫɫɤɨɝɨ ɹɡɵɤɚ ɧɚ
ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɩɫɟɜɞɨɤɨɞ ɜɵɝɥɹɞɢɬ ɬɚɤ:
ɡɚɞɚɬɶ ɧɚɱɚɥɶɧɵɟ ɩɪɢɛɥɢɠɟɧɢɹ x1,x2 ɜɧɭɬɪɢ ɢɧɬɟɪɜɚɥɚ a,b
ɪɚɫɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɞɥɹ ɧɢɯ
ɩɨɤɚ a-b > eps
ɟɫɥɢ ɮɭɧɤɰɢɹ(x1) >= ɮɭɧɤɰɢɹ(x2)
a = x1
ɢɧɚɱɟ
ɟɫɥɢ ɮɭɧɤɰɢɹ(x1) <= ɮɭɧɤɰɢɹ(x2)
a = x2
ɩɨɤɚ ɤɨɧɟɰ
ɡɚɞɚɬɶ ɧɨɜɵɟ ɧɚɱɚɥɶɧɵɟ ɩɪɢɛɥɢɠɟɧɢɹ x1,x2 ɜɧɭɬɪɢ ɧɨɜɨɝɨ ɢɧɬɟɪɜɚɥɚ a,b
ɪɚɫɫɱɢɬɚɬɶ ɧɨɜɵɟ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɞɥɹ ɧɢɯ
ɤɨɧɟɰ ɩɨɤɚ
ɋɚɦɵɣ ɜɚɠɧɵɣ ɜɨɩɪɨɫ – ɚ ɤɚɤ ɢɦɟɧɧɨ ɜɵɛɪɚɬɶ ɧɚɱɚɥɶɧɵɟ ɩɪɢɛɥɢɠɟɧɢɹ?
ɉɪɢɛɥɢɠɟɧɢɹ ɬɨɥɶɤɨ ɧɚɡɵɜɚɸɬɫɹ ɧɚɱɚɥɶɧɵɦɢ, ɧɚ ɤɚɠɞɨɦ ɫɥɟɞɭɸɳɟɦ
ɲɚɝɟ ɨɩɬɢɦɢɡɚɰɢɢ ɦɵ ɞɨɥɠɧɵ ɟɳɺ ɪɚɡ ɜɵɛɪɚɬɶ ɩɪɢɛɥɢɠɟɧɢɹ ɩɨ ɬɨɣ ɠɟ
ɫɚɦɨɣ ɫɯɟɦɟ. Ɉɛɳɢɣ ɩɪɢɧɰɢɩ ɜɵɛɨɪɚ – ɟɫɥɢ ɧɟ ɡɧɚɟɲɶ, ɤɚɤ ɜɵɛɪɚɬɶ
ɡɧɚɱɟɧɢɹ ɧɚ ɢɧɬɟɪɜɚɥɟ, ɞɟɥɢ ɩɨɪɨɜɧɭ. ȿɫɥɢ ɧɚɞɨ ɜɵɛɪɚɬɶ ɨɞɧɭ ɬɨɱɤɭ –
ɞɟɥɢ ɩɨɩɨɥɚɦ. ȿɫɥɢ ɞɜɟ ɬɨɱɤɢ, ɞɟɥɢ ɧɚ ɬɪɢ, ɢ ɬɚɤ ɞɚɥɟɟ. Ɍɨ ɟɫɬɶ ɞɥɹ ɧɚɲɟɝɨ
ɫɥɭɱɚɹ, ɤɨɝɞɚ ɢɧɬɟɪɜɚɥ
]100,100[ , ɩɟɪɜɵɟ ɩɪɢɛɥɢɠɟɧɢɹ ɜɵɛɢɪɚɸɬɫɹ ɤɚɤ
33.33,33.33 . Ɍɟɩɟɪɶ ɪɟɡɭɥɶɬɚɬ:
def opt( f, a,b, eps):
def ShowProcess():
print 'x1 = ', x1, ' x2 = ' , x2
stroka = 'SP. ' + 'a = ' + str(a) + ' b = ' + str(b)
print stroka
print f(a), f(x1), f(x2), f(b)
print
x1 = a + (b-a)/3
x2 = a + ((b-a)/3)*2
fa = f(a); fb = f(b)
fx1 = f(x1); fx2 = f(x2)
ShowProcess()
while ( abs(a-b) > eps):
if fx1 >= fx2:
a=x1;
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else: # if fx1 <= fx2:
b=x2;
x1 = a + (b-a)/3
x2 = a + ((b-a)/3)*2
fa = f(a); fb = f(b)
fx1 = f(x1); fx2 = f(x2)
ShowProcess()
x = a + (b-a)/2
return x
Ɍɟɩɟɪɶ ɡɚɞɚɱɚ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ. ɍɡɧɚɣɬɟ, ɤɚɤɢɟ ɟɳɺ ɛɵɜɚɸɬ
ɦɟɬɨɞɵ ɨɞɧɨɦɟɪɧɨɣ ɨɩɬɢɦɢɡɚɰɢɢ, ɜɵɛɟɪɢɬɟ ɩɨ ɜɤɭɫɭ ɢ ɪɟɚɥɢɡɭɣɬɟ. ɏɨɬɹ
ɛɵ ɦɟɬɨɞ ɡɨɥɨɬɨɝɨ ɫɟɱɟɧɢɹ.
Ɏɭɧɤɰɢɹ, ɭ ɤɨɬɨɪɨɣ ɦɧɨɝɨ ɩɚɪɚɦɟɬɪɨɜ
Ɇɧɨɝɨ, ɷɬɨ ɧɟ ɤɨɝɞɚ ɦɢɥɥɢɨɧ. Ɇɧɨɝɨ ɷɬɨ ɤɨɝɞɚ ɡɚɪɚɧɟɟ ɧɟ ɢɡɜɟɫɬɧɨ
ɫɤɨɥɶɤɨ. Ɇɨɠɧɨ ɢɯ, ɤɨɧɟɱɧɨ, ɫɨɛɪɚɬɶ ɫɧɚɱɚɥɚ ɜ ɫɩɢɫɨɤ ɢ ɩɟɪɟɞɚɬɶ ɤɚɤ
ɨɞɢɧ ɩɚɪɚɦɟɬɪ, ɧɨ ɦɨɠɧɨ ɢ ɬɚɤ, ɛɟɡ ɫɩɢɫɤɚ. ȼɵ ɡɧɚɟɬɟ, ɱɬɨ ɬɚɤɨɟ ɫɪɟɞɧɟɟ
ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ? ɉɪɚɜɢɥɶɧɨ, ɷɬɨ ɤɨɝɞɚ ɜɫɺ ɫɥɨɠɢɬɶ ɢ ɩɨɞɟɥɢɬɶ. Ɍɚɤ ɜɨɬ
ɷɬɨ ɦɵ ɩɪɨɝɪɚɦɦɢɪɨɜɚɬɶ ɧɟ ɛɭɞɟɦ. Ɇɵ ɛɭɞɟɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɬɶ ɫɪɟɞɧɟɟ
ɝɟɨɦɟɬɪɢɱɟɫɤɨɟ
n
xxxxxxg uuu ...)...,(
. ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɫɟ
2121
nn
ɱɢɫɥɚ ɞɨɥɠɧɵ ɛɵɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ, ɬɨ ɟɫɬɶ ɫɬɪɨɝɨ ɛɨɥɶɲɟ ɧɭɥɹ. Ⱥ
ɩɨɱɟɦɭ? Ɉɛɴɹɫɧɢɬɟ. ȼɨɬ ɩɪɨɝɪɚɦɦɧɵɣ ɤɨɞ, ɡɚɦɟɬɶɬɟ ɜ ɧɺɦ ɱɬɨ-ɬɨ ɧɨɜɨɟ:
def G( *xs):
result = 1
for x in xs:
result = result * x
result = result ** (1.0/len(xs))
return result
print 'G = ', G( 1,2,3 )
G = 1.81712059283
ɉɟɪɜɨɟ, ɱɬɨ ɛɪɨɫɚɟɬɫɹ ɜ ɝɥɚɡɚ, ɛɪɨɫɚɟɬɫɹ ɢɦɟɧɧɨ ɜ ɩɟɪɜɨɣ ɫɬɪɨɤɟ. Ⱥ
ɢɦɟɧɧɨ – ɡɜɺɡɞɨɱɤɚ ɩɟɪɟɞ ɢɦɟɧɟɦ ɟɞɢɧɫɬɜɟɧɧɨɝɨ ɩɚɪɚɦɟɬɪɚ. Ɉɧɚ ɨɡɧɚɱɚɟɬ,
ɱɬɨ ɜɧɭɬɪɢ ɮɭɧɤɰɢɢ ɫ ɷɬɢɦ ɩɚɪɚɦɟɬɪɨɦ ɦɨɠɧɨ ɨɛɪɚɳɚɬɶɫɹ ɤɚɤ ɫɨ ɫɩɢɫɤɨɦ.
ɇɟ ɫɨɜɫɟɦ, ɤɚɤ ɫɨ ɫɩɢɫɤɨɦ. Ɍɨɱɧɟɟ, ɫɨɜɫɟɦ ɧɟ ɤɚɤ ɫɨ ɫɩɢɫɤɨɦ. ɗɬɨɬ ɤɚɤ ɛɵ
ɫɩɢɫɨɤ ɦɨɠɧɨ ɬɨɥɶɤɨ ɱɢɬɚɬɶ, ɧɨ ɦɟɧɹɬɶ ɟɝɨ ɧɟɥɶɡɹ. ȼɩɪɨɱɟɦ, ɦɟɧɹɬɶ ɧɚɦ
162
ɟɝɨ ɢ ɧɟ ɧɚɞɨ, ɱɬɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ. ȿɫɥɢ ɜɚɦ ɰɢɤɥ ɤɚɠɟɬɫɹ ɧɟɨɱɟɜɢɞɧɵɦ,
ɦɨɠɧɨ ɟɝɨ ɡɚɦɟɧɢɬɶ ɧɚ ɞɪɭɝɨɣ, ɩɨɞɥɢɧɧɟɟ ɢ ɬɪɚɞɢɰɢɨɧɧɟɟ:
for i in xrange( 0, len(xs)):
result = result * xs[i]
Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɹ ɞɥɹ ɩɪɨɢɡɜɟɞɟɧɢɹ ɪɚɜɧɨ
ɟɞɢɧɢɰɟ. ɂ ɟɳɺ ɛɨɥɶɲɟ ɨɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ ɧɚ ɱɢɫɥɨ 1.0 – ɟɫɥɢ ɧɚɩɢɫɚɬɶ
ɩɪɨɫɬɨ 1, ɨɬɜɟɬ ɛɭɞɟɬ ɧɟɜɟɪɧɵɦ. Ɉɫɨɛɟɧɧɨɫɬɶ ɉɢɬɨɧɚ. ȿɫɥɢ ɯɨɬɢɬɟ
ɩɥɚɜɚɸɳɢɣ, ɜ ɫɦɵɫɥɟ ɞɪɨɛɧɵɣ, ɨɬɜɟɬ – ɢɫɩɨɥɶɡɭɣɬɟ ɜ ɜɵɱɢɫɥɟɧɢɹɯ
ɩɥɚɜɚɸɳɢɟ ɡɧɚɱɟɧɢɹ.
ɂ, ɪɚɡɭɦɟɟɬɫɹ, ɩɚɪɚɦɟɬɪɵ ɧɟ ɨɛɹɡɚɧɵ ɛɵɬɶ ɱɢɫɥɚɦɢ.
ɂ ɨɩɹɬɶ. Ʉɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ
ɉɪɢɨɛɪɟɬɹ ɧɨɜɵɟ ɡɧɚɧɢɹ, ɜɫɟɝɞɚ ɩɨɥɟɡɧɨ ɩɪɢɦɟɧɢɬɶ ɢɯ ɤ ɫɬɚɪɨɣ ɡɚɞɚɱɟ.
Ⱥɜɬɨɪ ɫ ɩɟɪɨɦ ɜ ɪɭɤɟ ɩɟɪɟɱɢɬɚɥ ɤɧɢɝɭ, ɧɚɩɢɫɚɧɧɭɸ ɫɜɵɲɟ ɬɪɢɞɰɚɬɢ ɥɟɬ
ɧɚɡɚɞ. ȼɦɟɲɚɬɶɫɹ ɜ ɩɪɨɢɡɜɟɞɟɧɢɟ ɬɚɤɨɣ ɞɚɜɧɨɫɬɢ ɧɟ ɥɟɝɱɟ, ɱɟɦ ɜɬɨɪɢɱɧɨ
ɜɫɬɭɩɢɬɶ ɜ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɪɭɱɟɣ. Ɍɟɦ ɧɟ ɦɟɧɟɟ ɦɨɠɧɨ ɩɪɨɣɬɢ ɩɨ ɟɝɨ
ɨɛɦɟɥɟɜɲɟɦɭ ɪɭɫɥɭ, ɫɥɭɲɚɹ ɫɤɪɟɠɟɬ ɝɚɥɶɤɢ ɩɨɞ ɧɨɝɚɦɢ ɢ ɛɟɡ ɨɩɚɫɤɢ
ɡɚɝɥɹɞɵɜɚɹ ɜ ɨɦɭɬɵ, ɨɬɤɭɞɚ ɭɲɥɚ ɜɨɞɚ.
© Ʌɟɨɧɢɞ Ʌɟɨɧɨɜ, ɩɪɟɞɢɫɥɨɜɢɟ ɤ ɪɨɦɚɧɭ ȼɨɪ
Ɂɚɞɚɱɚ ɭɠɟ ɢɡɭɱɟɧɚ ɩɨ ɫɭɳɟɫɬɜɭ. Ɇɨɠɧɨ ɞɭɦɚɬɶ ɨ ɦɟɬɨɞɚɯ ɢ ɮɨɪɦɟ.
Ɉɮɨɪɦɢɦ ɪɟɲɟɧɢɟ ɤɜɚɞɪɚɬɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɜ ɜɢɞɟ ɮɭɧɤɰɢɢ. ɉɟɪɜɵɣ ɢ
ɝɥɚɜɧɵɣ ɜɨɩɪɨɫ ɩɪɢ ɧɚɩɢɫɚɧɢɢ ɥɸɛɨɣ ɮɭɧɤɰɢɢ – ɧɟ ɱɬɨ ɭ ɧɟɺ ɛɭɞɟɬ
ɜɧɭɬɪɢ. Ƚɥɚɜɧɵɣ ɜɨɩɪɨɫ – ɤɚɤɨɣ ɭ ɧɟɺ ɛɭɞɟɬ ɢɧɬɟɪɮɟɣɫ, ɱɬɨ ɛɭɞɟɬ ɧɚ ɜɯɨɞɟ
ɢ ɱɬɨ ɛɭɞɟɬ ɧɚ ɜɵɯɨɞɟ. Ⱦɥɹ ɮɭɧɤɰɢɢ, ɢɫɩɨɥɶɡɭɟɦɨɣ ɜ ɪɟɚɥɶɧɨɦ
ɩɪɢɥɨɠɟɧɢɢ, ɷɬɨ ɜɨ ɦɧɨɝɨɦ ɞɢɤɬɭɟɬɫɹ ɨɫɨɛɟɧɧɨɫɬɹɦɢ ɤɨɞɚ, ɢɡ ɤɨɬɨɪɨɝɨ
ɷɬɚ ɮɭɧɤɰɢɹ ɛɭɞɟɬ ɜɵɡɵɜɚɬɶɫɹ. ɇɚɲɚ ɮɭɧɤɰɢɹ ɩɢɲɟɬɫɹ ɜ ɱɢɫɬɨ ɭɱɟɛɧɵɯ
ɰɟɥɹɯ, ɩɨɷɬɨɦɭ ɜɫɺ ɧɚɦɧɨɝɨ ɩɪɨɳɟ.
ɇɚ ɜɯɨɞɟ – ɩɪɨɫɬɨ ɬɪɢ ɤɨɷɮɮɢɰɢɟɧɬɚ. ɋ ɜɵɯɨɞɨɦ ɫɥɨɠɧɟɟ. Ɏɭɧɤɰɢɹ
ɞɨɥɠɧɚ ɜɨɡɜɪɚɳɚɬɶ ɡɧɚɱɟɧɢɟ – ɧɢ, ɢɥɢ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɹ ɬɚɤ ɫɱɢɬɚɸ. ɍ
ɧɚɫ ɭɠɟ ɟɫɬɶ ɩɪɨɝɪɚɦɦɚ, ɩɨɦɟɳɚɸɳɚɹ ɧɚɣɞɟɧɧɵɟ ɤɨɪɧɢ ɜ ɫɩɢɫɨɤ. Ɉɱɟɧɶ
ɯɨɪɨɲɨ, ɟɝɨ ɢ ɛɭɞɟɦ ɜɨɡɜɪɚɳɚɬɶ. Ɇɨɠɧɨ ɛɵ ɷɬɢɦ ɢ ɨɝɪɚɧɢɱɢɬɶɫɹ. ɇɨ! ȿɫɥɢ
ɜ ɫɩɢɫɤɟ ɞɜɚ ɷɥɟɦɟɧɬɚ – ɤɨɪɧɟɣ ɞɜɚ, ɟɫɥɢ ɨɞɢɧ ɷɥɟɦɟɧɬ – ɬɨ ɤɨɪɟɧɶ ɨɞɢɧ. Ⱥ
ɟɫɥɢ ɫɩɢɫɨɤ ɩɭɫɬɨɣ, ɬɨ ɱɬɨ? ɗɬɨ ɭ ɧɚɫ ɤɨɪɧɟɣ ɧɟɬ ɢɥɢ ɷɬɨ ɭ ɧɚɫ ɬɨɠɞɟɫɬɜɨ?
163
ɉɨɷɬɨɦɭ ɧɟɥɶɡɹ ɨɬɤɚɡɵɜɚɬɶɫɹ ɨɬ ɬɟɤɫɬɨɜɨɝɨ ɨɩɢɫɚɧɢɹ ɪɟɡɭɥɶɬɚɬɚ.
ɉɪɟɞɥɚɝɚɸ ɞɨɛɚɜɢɬɶ ɟɝɨ ɜ ɫɩɢɫɨɤ ɩɨɫɥɟɞɧɢɦ ɷɥɟɦɟɧɬɨɦ. Ɉɯɨɬɧɨ
ɞɨɩɭɫɤɚɸ, ɱɬɨ ɜ ɪɟɚɥɶɧɨɣ ɩɪɨɝɪɚɦɦɟ ɷɬɨ ɨɤɚɡɚɥɨɫɶ ɛɵ ɧɟɭɞɨɛɧɵɦ, ɧɨ ɭ ɧɚɫ
ɩɨɤɚ ɧɟ ɪɟɚɥɶɧɚɹ ɩɪɨɝɪɚɦɦɚ. ɂɦɟɟɦ ɜɨɬ ɬɚɤɭɸ ɮɭɧɤɰɢɸ, ɜ ɩɟɪɜɨɦ
ɩɪɢɛɥɢɠɟɧɢɢ:
def QuaEq(A,B,C):
roots = []
result = 'ɬɚɤ, ɧɚ ɜɫɹɤɢɣ ɫɥɭɱɚɣ'
if A <> 0:
dis = B**2 - 4*A*C;
if dis > 0:
x1 = (-B+dis**0.5)/(2*A);
x2 = (-B-dis**0.5)/(2*A);
result = 'ɞɜɚ ɤɨɪɧɹ'
elif dis == 0:
x1 = (-B)/(2*A); x2 = x1
result = 'ɨɞɢɧ ɤɨɪɟɧɶ'
else:
x1 = 0; x2 = 0
roots.append(x1)
roots.append(x2)
elif B <> 0:
x1 = -C/B
result = 'ɨɞɢɧ ɤɨɪɟɧɶ'
roots.append(x1)
else:
if C == 0:
result = 'ɬɨɠɞɟɫɬɜɨ'
else:
result = 'ɤɨɪɧɟɣ ɧɟɬ'
roots.append(result)
return roots
ɂɦɹ ɮɭɧɤɰɢɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɤɪɚɳɟɧɢɟ ɨɬ ɫɥɨɜ quadratic equation –
ɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ. Ɉɛɪɚɬɢɬɟ ɟɳɺ ɪɚɡ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɜ ɫɩɢɫɤɟ ɦɨɝɭɬ
ɯɪɚɧɢɬɶɫɹ ɷɥɟɦɟɧɬɵ ɩɪɨɢɡɜɨɥɶɧɵɯ ɬɢɩɨɜ, ɱɬɨ ɞɥɹ ɧɚɫ ɨɱɟɧɶ ɭɞɨɛɧɨ.
Ɍɟɩɟɪɶ ɨ ɬɨɦ, ɤɚɤ ɷɬɭ ɮɭɧɤɰɢɸ ɜɵɡɜɚɬɶ ɢ ɤɚɤ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɟɺ
ɪɟɡɭɥɶɬɚɬɚɦɢ.
roots = QuaEq(3,10,3)
print roots[len(roots)-1]
for i in xrange(0,len(roots)-1):
print roots[i]
ɞɜɚ ɤɨɪɧɹ
164
-0.333333333333
-3.0
ɋɨɜɩɚɞɟɧɢɟ ɢɦɟɧɢ
roots ɜɧɭɬɪɢ ɮɭɧɤɰɢɢ ɢ ɢɦɟɧɢ roots ɫɧɚɪɭɠɢ,
ɪɚɡɭɦɟɟɬɫɹ, ɫɨɜɟɪɲɟɧɧɨ ɫɥɭɱɚɣɧɨ. Ɍɟɩɟɪɶ ɨ ɜɚɠɧɨɦ. Ⱦɥɹ ɷɬɢɯ ɩɚɪɚɦɟɬɪɨɜ
ɜɵɡɨɜɚ ɜɫɺ ɪɚɛɨɬɚɟɬ ɯɨɪɨɲɨ. Ⱥ ɜɨɬ ɞɥɹ ɞɪɭɝɢɯ ɜɵɥɟɡɚɟɬ ɫɬɚɪɚɹ ɩɪɨɛɥɟɦɚ ɫ
ɰɟɥɵɦɢ ɬɢɩɚɦɢ.
roots = QuaEq(0,5,3)
ɨɞɢɧ ɤɨɪɟɧɶ
-1
ɉɨɪɚ ɫ ɷɬɢɦ ɱɬɨ-ɬɨ ɫɞɟɥɚɬɶ. ɉɨɱɟɦɭ ɢɦɟɧɧɨ ɫɟɣɱɚɫ? ɉɨɬɨɦɭ ɱɬɨ ɧɚɲɟ
ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɨɮɨɪɦɥɟɧɨ ɜ ɜɢɞɟ ɮɭɧɤɰɢɢ. ȼɟɫɶ ɫɦɵɫɥ ɮɭɧɤɰɢɢ ɜ ɬɨɦ
ɢ ɡɚɤɥɸɱɚɟɬɫɹ, ɱɬɨ ɟɺ ɦɨɠɧɨ ɢ ɧɭɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɧɨɝɨɤɪɚɬɧɨ. Ⱥ ɡɧɚɱɢɬ,
ɧɚɲ ɫɤɨɪɛɧɵɣ ɬɪɭɞ ɧɟ ɩɪɨɩɚɞɺɬ.
ɉɪɟɞɥɚɝɚɸ ɪɟɲɢɬɶ ɩɪɨɛɥɟɦɭ ɫɚɦɵɦ ɧɟɡɚɬɟɣɥɢɜɵɦ ɫɩɨɫɨɛɨɦ. ɉɨɫɤɨɥɶɤɭ
ɦɵ ɧɟ ɯɨɬɢɦ ɡɚɞɚɜɚɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚɦ ɩɥɚɜɚɸɳɢɣ ɬɢɩ ɫɧɚɪɭɠɢ ɮɭɧɤɰɢɢ,
ɡɚɞɚɞɢɦ ɜɧɭɬɪɢ. ɇɟɦɧɨɝɨ ɢɡɦɟɧɢɦ ɫɚɦɨɟ ɧɚɱɚɥɨ ɩɪɨɝɪɚɦɦɧɨɝɨ ɤɨɞɚ.
ȼɦɟɫɬɨ
def QuaEq(A,B,C):
roots = []
ɧɚɩɢɲɟɦ
def QuaEq(A,B,C):
A = float(A); B = float(B); C = float(C)
roots = []
ɑɬɨ ɦɵ ɫɞɟɥɚɥɢ? Ɇɵ ɧɚɫɢɥɶɫɬɜɟɧɧɨ ɭɤɚɡɚɥɢ, ɱɬɨ ɜ ɩɟɪɟɦɟɧɧɵɯ
A,B,C
ɯɪɚɧɹɬɫɹ ɩɥɚɜɚɸɳɢɟ ɡɧɚɱɟɧɢɹ. ȿɫɬɟɫɬɜɟɧɧɨ, ɨɩɟɪɚɰɢɹ ɞɟɥɟɧɢɹ ɩɨɫɥɟ ɷɬɨɝɨ
ɜɵɞɚɥɚ ɬɪɟɛɭɟɦɵɣ ɧɚɦ ɩɥɚɜɚɸɳɢɣ – ɢ ɬɨɱɧɵɣ – ɪɟɡɭɥɶɬɚɬ. ȿɫɬɟɫɬɜɟɧɧɨ,
ɬɢɩ ɩɟɪɟɦɟɧɧɨɣ ɨɬ ɷɬɨɝɨ ɧɟ ɢɡɦɟɧɢɥɫɹ – ɩɨɬɨɦɭ ɱɬɨ ɭ ɩɟɪɟɦɟɧɧɨɣ ɬɢɩɚ
ɧɟɬ. ɇɟ ɦɨɝɭ ɭɞɟɪɠɚɬɶɫɹ ɨɬ ɨɱɟɪɟɞɧɨɣ ɨɱɟɧɶ ɭɦɟɫɬɧɨɣ ɰɢɬɚɬɵ:
ɉɨɬɨɦɭ ɱɬɨ ɯɨɱɭ ɜ ɭɛɨɪɧɭɸ,
Ⱥ ɭɛɨɪɧɵɯ ɜ Ɋɨɫɫɢɢ ɧɟɬ
© ɋɟɪɝɟɣ ȿɫɟɧɢɧ «ɋɬɪɚɧɚ ɧɟɝɨɞɹɟɜ
»
ɉɨɬɨɦɭ ɱɬɨ ɫ ɬɢɩɚɦɢ ɛɵɥɨ ɛɵ ɩɪɨɳɟ, ɧɨ ɬɢɩɨɜ ɜ ɉɢɬɨɧɟ ɧɟɬ. ɂ ɩɨɱɟɦɭ ɹ
ɬɚɤ ɩɨɞɪɨɛɧɨ ɧɚ ɷɬɨɦ ɨɫɬɚɧɚɜɥɢɜɚɸɫɶ ɭɠɟ ɜ ɱɟɬɜɺɪɬɨɣ ɩɨ ɫɱɺɬɭ ɝɥɚɜɟ?
165
ɉɨɬɨɦɭ ɱɬɨ ɷɬɨ ɨɱɟɧɶ ɜɚɠɧɨ ɞɥɹ ɩɨɧɢɦɚɧɢɹ ɉɢɬɨɧɚ. ɍ ɩɟɪɟɦɟɧɧɵɯ ɬɢɩɚ
ɧɟɬ. ɉɟɪɟɦɟɧɧɚɹ – ɷɬɨ ɩɪɨɫɬɨ ɹɳɢɤ, ɜ ɤɨɬɨɪɨɦ ɱɬɨ-ɬɨ ɥɟɠɢɬ. Ⱥ ɜɨɬ ɭ ɷɬɨɝɨ
ɱɬɨ-ɬɨ ɬɢɩ ɨɱɟɧɶ ɞɚɠɟ ɟɫɬɶ. Ɉɛɞɭɦɚɣɬɟ.
ɉɨɩɭɬɧɨ ɦɵ ɪɟɲɢɥɢ ɟɳɺ ɨɞɧɭ ɩɪɨɛɥɟɦɭ, ɫɚɦɢ ɬɨɝɨ ɧɟ ɡɚɦɟɬɢɜ. ɑɬɨ ɛɵɥɨ
ɛɵ, ɩɨɤɚ ɦɵ ɧɟ ɞɨɛɚɜɢɥɢ ɷɬɭ ɫɬɪɨɤɭ, ɩɪɢ ɬɚɤɨɦ ɜɵɡɨɜɟ:
roots = QuaEq( '3', '10', '3')
ɉɪɚɜɢɥɶɧɨ, ɫɨɨɛɳɟɧɢɟ ɨɛ ɨɲɢɛɤɟ ɜɨ ɜɪɟɦɹ ɢɫɩɨɥɧɟɧɢɹ ɩɪɨɝɪɚɦɦɵ. Ⱥ
ɬɟɩɟɪɶ ɜɫɺ ɨɬɥɢɱɧɨ ɪɚɛɨɬɚɟɬ – ɧɚɲɚ ɞɨɛɚɜɥɟɧɧɚɹ ɫɬɪɨɤɚ ɤɨɞɚ ɩɪɟɨɛɪɚɡɭɟɬ
ɫɬɪɨɤɨɜɵɟ ɡɧɚɱɟɧɢɹ ɜ ɩɥɚɜɚɸɳɢɟ. ɉɪɟɨɛɪɚɡɭɟɬ ɩɨɬɨɦɭ, ɱɬɨ ɢɯ ɦɨɠɧɨ
ɩɪɟɨɛɪɚɡɨɜɚɬɶ.
Ⱦɚɥɶɲɟ ɯɭɠɟ. Ɍɢɩɨɜ ɧɟɬ. ɇɚ ɜɯɨɞ ɮɭɧɤɰɢɢ ɦɨɠɧɨ ɡɚɞɚɬɶ ɱɬɨ ɭɝɨɞɧɨ, ɥɢɲɶ
ɛɵ ɩɚɪɚɦɟɬɪɨɜ ɛɵɥɨ ɬɪɢ. ɇɚɩɪɢɦɟɪ, ɜɨɬ ɬɚɤɨɟ:
roots = QuaEq( 'Ⱥ ɩɨɱɟɦɭ ɭ ɬɟɛɹ ɬɚɤɢɟ ɛɨɥɶɲɢɟ ɭɲɢ?',
'Ⱥ ɩɨɱɟɦɭ ɭ ɬɟɛɹ ɬɚɤɢɟ ɛɨɥɶɲɢɟ ɝɥɚɡɚ',
'Ⱥ ɩɨɬɨɦɭ ɱɬɨ ɤɚɤɚɸ')
Ɍɚɤ ɧɟ ɩɪɨɣɞɺɬ – ɜɵɥɟɬɚɟɬ ɧɚ ɩɨɫɥɟɞɧɟɣ ɫɬɪɨɤɟ, ɱɬɨ ɯɚɪɚɤɬɟɪɧɨ. Ʉɨɧɟɱɧɨ,
ɜɵ ɫɨɜɟɪɲɟɧɧɨ ɬɨɱɧɨ ɩɨɦɧɢɬɟ, ɤɚɤɨɝɨ ɬɢɩɚ ɩɚɪɚɦɟɬɪɵ ɧɭɠɧɨ ɡɚɞɚɬɶ ɧɚ
ɜɯɨɞ ɜɚɲɟɣ ɮɭɧɤɰɢɢ ɢ ɧɢɤɨɝɞɚ ɧɟ ɨɲɢɛɺɬɟɫɶ. ɇɨ ɧɚɞɨ ɩɪɟɞɩɨɥɚɝɚɬɶ ɫ
ɫɚɦɨɝɨ ɧɚɱɚɥɚ, ɱɬɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɧɚɲɟɣ ɮɭɧɤɰɢɟɣ ɛɭɞɟɦ ɧɟ ɬɨɥɶɤɨ ɦɵ, ɧɨ ɢ
ɤɚɤɢɟ-ɬɨ ɞɪɭɝɢɟ ɧɟɩɪɢɹɬɧɵɟ ɧɚɦ ɥɸɞɢ. ɂ ɷɬɢ ɥɸɞɢ ɫɨɜɟɪɲɟɧɧɨ
ɨɛɹɡɚɬɟɥɶɧɨ ɡɚɞɚɞɭɬ ɧɚ ɜɯɨɞ ɧɚɲɟɣ ɮɭɧɤɰɢɢ ɫɨɜɟɪɲɟɧɧɨ ɧɟɭɦɟɫɬɧɵɟ ɢ
ɧɟɥɟɩɵɟ ɩɚɪɚɦɟɬɪɵ.
Ɉɞɧɚɤɨ ɧɚɩɨɦɢɧɚɸ, ɬɢɩ ɩɟɪɟɦɟɧɧɨɣ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɜɟɪɟɧ.
if (type(A) <> int) and (type(A) <> float):
print 'ȼɫɺ ɩɪɨɩɚɥɨ'
Ɂɞɟɫɶ ɦɵ ɬɨɥɶɤɨ ɜɵɜɨɞɢɦ ɩɚɧɢɱɟɫɤɨɟ ɫɨɨɛɳɟɧɢɟ. Ⱦɨɛɚɜɶɬɟ ɩɪɨɜɟɪɤɭ
ɬɢɩɨɜ ɞɜɭɯ ɞɪɭɝɢɯ ɜɯɨɞɧɵɯ ɩɚɪɚɦɟɬɪɨɜ. Ɉɮɨɪɦɢɬɟ ɜɫɸ ɩɪɨɜɟɪɤɭ ɜ ɜɢɞɟ
ɮɭɧɤɰɢɢ, ɜɨɡɜɪɚɳɚɸɳɟɣ ɛɭɥɟɜɫɤɢɣ ɪɟɡɭɥɶɬɚɬ. ȼɵɡɨɜɢɬɟ ɷɬɭ ɮɭɧɤɰɢɸ ɜ
ɧɚɱɚɥɟ ɬɨɣ ɮɭɧɤɰɢɢ ɢ ɩɪɢɦɟɧɢɬɟ ɭɫɥɨɜɧɵɣ ɨɩɟɪɚɬɨɪ. ɉɨɤɚ ɜɫɺ.
166
Ƚɥɚɜɚ ɜɨɫɶɦɚɹ, ɤɨɪɨɬɤɚɹ. Ɇɨɞɭɥɢ. Ʉɨɪɨɬɤɨ
GED
Ʉɨɪɨɬɤɨ ɧɟ ɩɨɬɨɦɭ, ɱɬɨ ɧɟɜɚɠɧɨ. Ɇɨɞɭɥɢ – ɷɬɨ ɨɱɟɧɶ ɜɚɠɧɨ. ɇɨ ɜ ɉɢɬɨɧɟ
ɢɞɟɹ ɦɨɞɭɥɟɣ ɪɟɚɥɢɡɨɜɚɧɚ ɨɫɟɧɶ ɩɪɨɫɬɨ. Ɋɚɡɭɦɟɟɬɫɹ, ɤɚɤ ɢ ɜɫɟɝɞɚ, ɟɫɬɶ
ɯɢɬɪɵɟ ɧɚɜɨɪɨɬɵ, ɧɨ ɫɚɦɚ ɨɫɧɨɜɚ ɧɚɫɬɨɥɶɤɨ ɩɪɨɫɬɚ, ɱɬɨ ɩɪɨɳɟ ɩɪɨɫɬɨ ɛɵɬɶ
ɧɟ ɦɨɠɟɬ.
ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ
ɉɪɟɠɞɟ ɱɟɦ ɪɟɲɢɬɶ ɩɪɨɛɥɟɦɭ, ɧɚɞɨ ɟɺ ɧɚɣɬɢ, ɧɚɫɬɭɩɢɬɶ ɧɚ ɝɪɚɛɥɢ ɢ
ɨɫɨɡɧɚɬɶ. Ⱦɥɹ ɧɚɱɚɥɚ ɧɚɩɢɲɟɦ ɧɟɜɟɪɨɹɬɧɨ ɩɪɨɫɬɭɸ, ɧɨ ɜɩɨɥɧɟ
ɩɪɚɤɬɢɱɟɫɤɢ ɩɪɢɦɟɧɢɦɭɸ ɮɭɧɤɰɢɸ. Ɉɧɚ ɛɭɞɟɬ ɜɵɱɢɫɥɹɬɶ ɩɥɨɳɚɞɶ
ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɩɨ ɤɚɬɟɬɚɦ. ɇɚ ɜɫɹɤɢɣ ɫɥɭɱɚɣ ɧɚɩɨɦɢɧɚɸ –
ɫɬɨɪɨɧɵ ɬɪɟɭɝɨɥɶɧɢɤɚ ɬɪɚɞɢɰɢɨɧɧɨ ɨɛɨɡɧɚɱɚɸɬɫɹ ɤɚɤ
. ɑɬɨ ɜɚɠɧɨ, ɩɪɨɬɢɜ ɭɝɥɚ D ɧɚɯɨɞɢɬɫɹ ɫɬɨɪɨɧɚ a, ɩɪɨɬɢɜ ɭɝɥɚ E –
,,
b
ɫɬɨɪɨɧɚ
ɬɪɟɭɝɨɥɶɧɢɤɟ ɝɢɩɨɬɟɧɭɡɚ ɨɛɨɡɧɚɱɚɟɬɫɹ ɤɚɤ
, ɚ ɩɪɨɬɢɜ ɫɬɨɪɨɧɵ c – ɩɨɱɟɦɭ-ɬɨ ɭɝɨɥ G. ȼ ɩɪɹɦɨɭɝɨɥɶɧɨɦ
c, ɚ ɤɚɬɟɬɵ ba, .
Ɏɨɪɦɭɥɚ ɜɨɬ:
ab
. ə ɨɛɟɳɚɥ, ɱɬɨ ɛɭɞɟɬ ɨɱɟɧɶ ɩɪɨɫɬɨ. Ⱥ ɬɟɩɟɪɶ
s
2
ɮɭɧɤɰɢɹ:
def S_1(a,b):
return (a*b)/2
ɉɨɱɟɦɭ ɮɭɧɤɰɢɹ ɧɚɡɵɜɚɟɬɫɹ
S_1 – ɩɨɬɨɦɭ, ɱɬɨ ɛɭɞɟɬ S_2. Ⱥ ɩɨɱɟɦɭ ɛɟɡ
ɮɚɧɬɚɡɢɢ ɢ ɨɞɧɨɨɛɪɚɡɧɨ?
– Ⱦɨɪɨɝɚɹ, ɧɭ ɩɪɢɞɭɦɚɣ ɱɬɨ-ɧɢɛɭɞɶ, ɬɵ ɠɟ ɭ ɦɟɧɹ ɬɚɤɚɹ ɮɚɧɬɚɡɺɪɤɚ!
© ɋɬɚɪɵɣ, ɧɨ ɫɦɟɲɧɨɣ ɚɧɟɤɞɨɬ
Ɏɨɪɦɭɥɵ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɷɬɨɣ ɠɟ ɩɥɨɳɚɞɢ ɟɫɬɶ ɢ ɞɪɭɝɢɟ, ɭɠɟ ɫ
ɩɪɢɦɟɧɟɧɢɟɦ ɬɪɢɝɨɧɨɦɟɬɪɢɢ. ȼɨɬ ɞɜɟ. ɉɟɪɜɚɹ ɜɵɱɢɫɥɹɟɬ ɩɥɨɳɚɞɶ ɩɨ
ɤɚɬɟɬɭ ɢ ɭɝɥɭ. ȼɬɨɪɚɹ – ɩɨ ɝɢɩɨɬɟɧɭɡɟ ɢ ɭɝɥɭ. ɍɝɨɥ, ɩɨɧɹɬɧɨɟ ɞɟɥɨ, ɧɟ
ɩɪɹɦɨɣ.
2
E
tga
s
2
cba ..
, ɚ ɭɝɥɵ ɤɚɤ
167
2
c
s
DD
cossin
2
Ɏɭɧɤɰɢɢ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɱɭɬɶ ɫɥɨɠɧɟɟ, ɧɨ ɧɟ ɧɚɦɧɨɝɨ.
import math
def S_2(a,ugol):
return ((a**2)* math.tan(ugol))/2
def S_3(c,ugol):
return (c**2*math.sin(ugol)*math.cos(ugol))/2
Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ ɧɚ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɢɦɩɨɪɬɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɭɥɹ.
ɍɝɥɵ ɧɚɞɨ ɡɚɞɚɜɚɬɶ ɜ ɪɚɞɢɚɧɚɯ. ȿɫɥɢ ɭɝɨɥ ɭ ɧɚɫ ɜ ɝɪɚɞɭɫɚɯ, ɧɚɞɨ ɩɪɢ
ɜɵɡɨɜɟ ɩɟɪɟɜɟɫɬɢ ɟɝɨ ɜ ɪɚɞɢɚɧɵ. ȼɨɬ ɷɬɢ ɬɪɢ ɜɵɡɨɜɚ ɬɪɺɯ ɮɭɧɤɰɢɣ
ɜɵɱɢɫɥɹɸɬ ɩɥɨɳɚɞɶ ɨɞɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɬɪɟɭɝɨɥɶɧɢɤɚ, ɧɭ ɢɥɢ ɩɨɱɬɢ ɬɨɝɨ ɠɟ,
ɩɨɬɨɦɭ ɱɬɨ ɭɝɥɵ ɹ ɨɤɪɭɝɥɢɥ ɞɨ ɰɟɥɵɯ ɝɪɚɞɭɫɨɜ. ɗɬɨ ɉɢɮɚɝɨɪɨɜ
ɬɪɟɭɝɨɥɶɧɢɤ, ɫɨ ɫɬɨɪɨɧɚɦɢ (3.4,5).
s = S_1(3,4)
s = S_2(3,math.radians(53))
s = S_3(5,math.radians(53))
ɏɨɬɹ ɮɭɧɤɰɢɢ ɨɱɟɧɶ ɩɪɨɫɬɵɟ, ɧɨ ɨɱɟɧɶ ɩɨɥɟɡɧɵɟ ɢ, ɫɤɨɪɟɟ ɜɫɟɝɨ, ɦɨɝɭɬ
ɩɨɧɚɞɨɛɢɬɶɫɹ ɟɳɺ ɢ ɟɳɺ ɪɚɡ. Ɇɨɠɧɨ, ɪɚɡɭɦɟɟɬɫɹ, ɩɪɢɤɨɩɚɬɶ ɢɫɯɨɞɧɵɣ
ɬɟɤɫɬ, ɚ ɩɨɬɨɦ, ɤɨɝɞɚ ɨɱɟɧɶ ɩɨɧɚɞɨɛɢɬɫɹ, ɢɡɜɥɟɤɚɬɶ ɟɝɨ ɢɡ ɪɭɤɚɜɚ ɢ
ɜɫɬɚɜɥɹɬɶ ɜ ɧɭɠɧɨɟ ɦɟɫɬɨ, ɧɨ ɦɧɟ ɷɬɨ ɤɚɠɟɬɫɹ ɤɚɤɢɦ-ɬɨ ɧɟɩɪɚɜɢɥɶɧɵɦ.
ȼɟɞɶ ɤɨɝɞɚ ɜ ɬɨɦ ɤɨɞɟ, ɱɬɨ ɜɜɟɪɯɭ, ɦɵ ɜɵɱɢɫɥɹɟɦ ɫɢɧɭɫ, ɦɵ ɧɟ ɜɫɬɚɜɥɹɟɦ
ɱɟɣ-ɬɨ ɝɪɹɡɧɵɣ ɩɪɨɝɪɚɦɦɧɵɣ ɤɨɞ ɜ ɧɚɲ ɛɟɥɨɫɧɟɠɧɵɣ. Ɇɵ ɩɪɨɫɬɨ ɩɢɲɟɦ
import math ɢ ɩɨɫɥɟ ɷɬɨɝɨ ɩɨɥɭɱɚɟɦ ɞɨɫɬɭɩ ɤ ɫɢɧɭɫɚɦ ɢ ɩɪɨɱɟɦɭ ɛɨɝɚɬɫɬɜɭ.
ɏɨɬɟɥɨɫɶ ɛɵ ɢ ɧɚɦ ɬɚɤ ɠɟ.
Ɇɚɥɟɧɶɤɨɟ ɡɚɦɟɱɚɧɢɟ. Ʌɢɱɧɨ ɦɨɺ ɦɧɟɧɢɟ – ɧɚɡɧɚɱɟɧɢɟ ɦɨɞɭɥɟɣ
ɡɚɤɥɸɱɚɟɬɫɹ ɩɨɱɬɢ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɜ ɬɨɦ, ɱɬɨɛɵ, ɧɚɩɢɫɚɜ ɱɬɨ-ɬɨ ɯɨɪɨɲɟɟ ɢ
ɩɨɥɟɡɧɨɟ, ɢɦɟɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɷɬɨ ɟɳɺ ɢ ɟɳɺ ɪɚɡ. ɍ ɞɪɭɝɢɯ
ɚɜɬɨɪɨɜ ɦɨɝɭɬ ɛɵɬɶ ɞɪɭɝɢɟ ɦɧɟɧɢɹ.
Ɋɟɲɟɧɢɟ ɡɚɞɚɱɢ
Ɍɚɤ ɤɚɤ ɫɞɟɥɚɬɶ ɢɡ ɧɚɲɢɯ ɬɪɺɯ ɮɭɧɤɰɢɣ ɩɨɥɧɨɰɟɧɧɵɣ ɦɨɞɭɥɶ ɞɥɹ
ɩɨɫɬɨɹɧɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ? Ⱦɚ ɩɨɱɬɢ ɧɢɤɚɤ! ɇɟ ɜ ɫɦɵɫɥɟ, ɱɬɨ ɷɬɨ ɩɨɱɬɢ
168
ɧɟɜɨɡɦɨɠɧɨ. ȼ ɫɦɵɫɥɟ, ɱɬɨ ɷɬɨ ɧɟ ɬɪɟɛɭɟɬ ɩɨɱɬɢ ɧɢɤɚɤɢɯ ɭɫɢɥɢɣ. Ɇɵ
ɛɟɪɺɦ ɜɨɬ ɷɬɨɬ ɤɨɞ
import math
def S_1(a,b):
return (a*b)/2
def S_2(a,ugol):
return ((a**2)* math.tan(ugol))/2
def S_3(c,ugol):
return (c**2*math.sin(ugol)*math.cos(ugol))/2
ɢ ɫɨɯɪɚɧɹɟɦ ɟɝɨ ɜ ɮɚɣɥ ɩɨɞ ɢɦɟɧɟɦ
ɱɬɨ ɭ ɧɚɫ ɬɨɥɶɤɨ ɬɪɢ ɮɭɧɤɰɢɢ, ɷɬɨ ɫɨɤɪɚɳɟɧɢɟ ɨɬ ɫɥɨɜɚ
triMod.py. tri – ɷɬɨ ɧɟ ɜ ɬɨɦ ɫɦɵɫɥɟ,
triangle. ȼɫɺ.
Ɇɨɞɭɥɶ ɝɨɬɨɜ. ɉɨɜɟɪɶɬɟ, ɜ ɞɪɭɝɢɯ ɹɡɵɤɚɯ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɫɨɡɞɚɧɢɟ
ɦɨɞɭɥɹ ɬɪɟɛɭɟɬ ɡɚɦɟɬɧɨ ɛɨ
ғɥɶɲɢɯ ɭɫɢɥɢɣ. Ɍɟɩɟɪɶ ɨ ɬɨɦ, ɤɚɤ ɧɚɦ ɟɝɨ
ɢɫɩɨɥɶɡɨɜɚɬɶ. ɗɬɨ ɱɭɬɶ ɫɥɨɠɧɟɟ. ȼɨɬ ɬɪɢ ɜɵɡɨɜɚ ɬɪɺɯ ɮɭɧɤɰɢɣ:
import triMod
import math
s = triMod.S_1(3,4)
print s
s = triMod.S_2(3,math.radians(53))
print s
s = triMod.S_3(5,math.radians(53))
print s
Ɂɞɟɫɶ ɭɠɟ ɟɫɬɶ ɧɚ ɱɬɨ ɨɛɪɚɬɢɬɶ ɜɧɢɦɚɧɢɟ. ɉɨɹɜɢɥɚɫɶ ɫɬɪɨɤɚ
import triMod.
ɉɟɪɟɞ ɢɦɟɧɚɦɢ ɜɵɡɵɜɚɟɦɵɯ ɮɭɧɤɰɢɣ ɩɨɹɜɢɥɨɫɶ ɭɬɨɱɧɟɧɢɟ, ɤ ɤɚɤɨɦɭ
ɦɨɞɭɥɸ ɨɧɢ ɩɪɢɧɚɞɥɟɠɚɬ. ɗɬɨ ɨɠɢɞɚɟɦɨ ɢ ɩɨɧɹɬɧɨ. Ɍɟɩɟɪɶ ɨ ɜɚɠɧɨɦ. Ʉɚɤ
ɜɢɞɢɬɟ, ɜɫɺ ɩɨɥɭɱɢɥɨɫɶ ɛɵɫɬɪɨ ɢ ɨɱɟɧɶ ɩɪɨɫɬɨ. ɇɨ, ɤɚɤ ɜɫɟɝɞɚ, ɟɫɬɶ
ɧɸɚɧɫɵ.
ɉɟɪɜɵɣ, ɛɟɡɨɛɢɞɧɵɣ. ɇɚɲ ɦɨɞɭɥɶ ɫɫɵɥɚɟɬɫɹ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɧɚ ɦɨɞɭɥɶ
math. ɗɬɨ ɩɨɧɹɬɧɨ, ɜɟɞɶ ɧɚɦ ɧɭɠɟɧ ɫɢɧɭɫ ɢ ɩɪɨɱɢɟ ɬɚɧɝɟɧɫɵ. Ƚɨɥɨɜɧɚɹ
ɩɪɨɝɪɚɦɦɚ ɬɨɠɟ ɫɫɵɥɚɟɬɫɹ ɧɚ ɬɨɬ ɠɟ ɦɨɞɭɥɶ
math. Ɍɚɤ ɜɨɬ, ɨɧɚ
ɢɦɩɨɪɬɢɪɭɟɬ ɟɝɨ ɧɟ ɩɨɬɨɦɭ, ɱɬɨ ɨɧ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɢɦɩɨɪɬɢɪɭɟɦɨɦ ɟɸ
ɦɨɞɭɥɟ
triMod, ɚ ɩɨɬɨɦɭ, ɱɬɨ ɨɧɚ, ɝɨɥɨɜɧɚɹ ɩɪɨɝɪɚɦɦɚ, ɢɫɩɨɥɶɡɭɟɬ ɟɝɨ ɫɚɦɚ
– ɜ ɩɪɨɰɟɫɫɟ ɩɟɪɟɜɨɞɚ ɝɪɚɞɭɫɨɜ ɜ ɪɚɞɢɚɧɵ. Ƚɨɜɨɪɹ ɩɨ-ɞɪɭɝɨɦɭ, ɟɫɥɢ
ɦɨɞɭɥɶ
ɦɨɞɭɥɶ
A ɢɦɩɨɪɬɢɪɭɟɬ ɦɨɞɭɥɶ B, ɚ ɦɨɞɭɥɶ B, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɢɦɩɨɪɬɢɪɭɟɬ
C, ɬɨ ɦɨɞɭɥɶ A ɜɨɜɫɟ ɧɟ ɨɛɹɡɚɧ ɢɦɩɨɪɬɢɪɨɜɚɬɶ ɦɨɞɭɥɶ C. Ʉɨɧɤɪɟɬɧɨ
169
ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɷɬɨ ɡɧɚɱɢɬ, ɱɬɨ ɟɫɥɢ ɛɵ ɧɚɦ ɧɟ ɧɭɠɧɨ ɛɵɥɨ ɜɵɡɵɜɚɬɶ
ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɜ ɪɚɞɢɚɧɵ, ɬɨ ɫɬɪɨɤɭ
import math ɜ ɝɨɥɨɜɧɨɣ ɩɪɨɝɪɚɦɦɟ
ɦɨɠɧɨ ɛɵɥɨ ɛɵ ɭɞɚɥɢɬɶ. ɗɬɨ ɯɨɪɨɲɚɹ ɧɨɜɨɫɬɶ, ɩɨɬɨɦɭ ɱɬɨ ɭɩɪɨɳɚɟɬ
ɩɪɨɰɟɫɫ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ.
Ɍɟɩɟɪɶ ɩɥɨɯɚɹ. ɍ ɦɟɧɹ ɧɚ ɞɢɫɤɟ ɟɫɬɶ ɤɚɬɚɥɨɝ/ɞɢɪɟɤɬɨɪɢɹ/ɤɚɤ ɜɚɦ ɭɝɨɞɧɨ.
ɂɦɹ ɭ ɧɟɝɨ ɱɬɨ-ɬɨ ɜɪɨɞɟ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɸ \ ɤɨɧɤɪɟɬɧɨ ɉɢɬɨɧ \ sources. ɇɭ, ɜɵ ɩɨɧɹɥɢ, ɹ ɱɟɥɨɜɟɤ
D:\Ɇɨɢ ɝɟɧɢɚɥɶɧɵɟ ɤɧɢɝɢ \ Ƚɟɧɢɚɥɶɧɵɟ ɤɧɢɝɢ ɩɨ
ɨɱɟɧɶ ɫɤɪɨɦɧɵɣ. Ɍɚɤ ɜɨɬ, ɜɫɟ ɢɫɯɨɞɧɵɟ ɬɟɤɫɬɵ ɭ ɦɟɧɹ ɯɪɚɧɹɬɫɹ ɜ ɷɬɨɦ
ɤɚɬɚɥɨɝɟ. ɋɪɟɞɢ ɧɢɯ ɝɨɥɨɜɧɚɹ ɩɪɨɝɪɚɦɦɚ ɩɨɞ ɢɦɟɧɟɦ
triMod.py.
main.py ɢ ɧɚɲ ɦɨɞɭɥɶ
# ɡɚɩɨɡɞɚɥɨɟ ɪɚɡɴɹɫɧɟɧɢɟ
ɉɨɱɟɦɭ
ɝɨɥɨɜɧɚɹ ɩɪɨɝɪɚɦɦɚ? Ƚɨɥɨɜɧɚɹ ɩɪɨɝɪɚɦɦɚ – ɷɬɨ ɬɚ ɲɬɭɤɚ, ɤɨɬɨɪɚɹ
ɜɵɡɵɜɚɟɬ ɜɫɟɯ, ɚ ɟɺ ɧɢɤɬɨ ɧɟ ɜɵɡɵɜɚɟɬ, ɤɪɨɦɟ ɩɨɥɶɡɨɜɚɬɟɥɹ.
Ɇɭɠɱɢɧɵ ɥɸɛɹɬ ɠɟɧɳɢɧ
ɀɟɧɳɢɧɵ ɥɸɛɹɬ ɞɟɬɟɣ
Ⱦɟɬɢ ɥɸɛɹɬ ɯɨɦɹɱɤɨɜ
ɂ ɬɨɥɶɤɨ ɯɨɦɹɱɤɢ ɧɢɤɨɝɨ ɧɟ ɥɸɛɹɬ
# ɤɨɧɟɰ Ɂɚɩɨɡɞɚɥɨɝɨ
ɂ ɜɫɺ ɨɬɥɢɱɧɨ ɪɚɛɨɬɚɟɬ. ɇɚ ɫɚɦɨɦ ɞɟɥɟ, ɜɫɺ ɝɨɪɚɡɞɨ ɫɥɨɠɧɟɟ ɢ ɪɚɛɨɬɚɟɬ ɜɫɺ
ɨɬɥɢɱɧɨ ɬɨɥɶɤɨ ɩɨɬɨɦɭ, ɱɬɨ ɨɛɚ ɬɟɤɫɬɚ ɩɪɨɝɪɚɦɦ ɪɚɡɦɟɳɟɧɵ ɜ ɨɞɧɨɦ
ɤɚɬɚɥɨɝɟ. Ⱥ ɟɫɥɢ ɧɟɬ? ȼ ɉɢɬɨɧɟ ɪɟɚɥɢɡɨɜɚɧ ɞɨɜɨɥɶɧɨ ɫɥɨɠɧɵɣ ɚɥɝɨɪɢɬɦ
ɩɨɢɫɤɚ ɩɨɞɤɥɸɱɚɟɦɨɝɨ ɦɨɞɭɥɹ. Ⱦɥɹ ɭɱɟɛɧɵɯ ɡɚɞɚɱ, ɜɪɨɞɟ ɧɚɲɟɣ, ɷɬɨ
ɧɟɚɤɬɭɚɥɶɧɨ. ȼ ɪɟɚɥɶɧɨɣ ɠɢɡɧɢ, ɫɤɨɪɟɟ ɜɫɟɝɨ, ɢɫɩɨɥɶɡɭɟɦɵɟ ɜɚɦɢ – ɢ
ɜɫɟɦɢ – ɦɨɞɭɥɢ ɛɭɞɭɬ ɥɟɠɚɬɶ ɜ ɤɚɤɨɦ-ɬɨ ɨɞɧɨɦ ɤɚɬɚɥɨɝɟ. ɉɪɨɝɪɚɦɦɵ,
ɢɫɩɨɥɶɡɭɸɳɢɟ ɷɬɢ ɦɨɞɭɥɢ, ɛɭɞɭɬ ɧɚɜɟɪɧɹɤɚ ɯɪɚɧɢɬɶɫɹ ɜ ɫɨɜɫɟɦ ɞɪɭɝɢɯ
ɤɚɬɚɥɨɝɚɯ. ɇɨ ɷɬɨ, ɤɚɤ ɩɪɢɧɹɬɨ ɜɵɪɚɠɚɬɶɫɹ, –
ɨɛɫɭɠɞɚɟɦɵɯ ɜ ɧɚɲɟɣ ɤɧɢɝɟ ɬɟɦ
.
ɞɚɥɟɤɨ ɜɵɯɨɞɢɬ ɡɚ ɪɚɦɤɢ
ɑɬɨ ɟɳɺ ɜɚɠɧɨ ɡɧɚɬɶ
Ɋɚɡɪɨɡɧɟɧɧɵɟ ɡɚɦɟɱɚɧɢɹ ɨ ɦɨɞɭɥɹɯ. Ɂɞɟɫɶ ɨ ɬɨɦ, ɛɟɡ ɱɟɝɨ ɦɨɠɧɨ ɢ
ɨɛɨɣɬɢɫɶ, ɧɨ ɥɭɱɲɟ ɜɫɺ ɠɟ ɡɧɚɬɶ.
ɉɟɪɜɨɟ ɡɚɦɟɱɚɧɢɟ. ɍ ɧɚɫ ɩɪɨɝɪɚɦɦɚ ɢɦɩɨɪɬɢɪɭɟɬ ɧɚɩɢɫɚɧɧɵɣ ɧɚɦɢ
ɦɨɞɭɥɶ, ɤɨɬɨɪɵɣ ɢɦɩɨɪɬɢɪɭɟɬ ɦɨɞɭɥɶ
math, ɤɨɬɨɪɵɣ ɦɵ ɧɟ ɩɢɫɚɥɢ, ɢ
ɢɫɯɨɞɧɵɣ ɬɟɤɫɬ, ɤɨɬɨɪɨɝɨ ɞɚɠɟ ɧɟ ɜɢɞɚɥɢ. ȼɩɨɥɧɟ ɜɨɡɦɨɠɧɨ, ɱɬɨ ɦɵ ɟɝɨ ɢ
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