三角边求和程序

Question

So in math class we had this problem:

You are given a triangle with sides 4 units long. Inside the triangle, there are smaller triangles made from the midsegments of the larger triangles. There are 8 total inscribed triangles. What are the total side lengths?

So, I decided to see if I could write a python program that could solve this for all number of triangles and all side lengths.

Here it is:

tri = int(raw_input("How many triangles are there?\n>"))
size = int(raw_input("What is the side length of the biggest triangle?\n>"))
tot = 0
for i in range(1, tri):
    tot += 3*(float(size/i))
print str(tot)

I tried it with tri = 8 and size = 4, as in the original problem, and got 24.0 . As wolfram alpha shows us, that is wrong .

To try to clarify what happened in each step, I edited it to:

tri = int(raw_input("How many triangles are there?\n>"))
size = int(raw_input("What is the side length of the biggest triangle?\n>"))
tot = 0
for i in range(1, tri):
    tot += 3*(float(size/i+0.0000001))
    print str(tot)
print str(tot)

The output was:

12.0000003
18.0000006
21.0000009
24.0000012
24.0000015
24.0000018
24.0000021
24.0000021

Anyone think they know where I went wrong?

Answer 1

You are not looping tri times:

for i in range(1, tri):

The end value is not included, so you are counting 1 through to 7 here, not 8 . Remove the 1 and add 1 in the loop:

for i in range(tri):
    tot += 3.0 * size / (i + 1)

You just need one float value in the calculation, turning 3 into 3.0 does this for us. Unfortunately, in Python 2, / will use integer or floor division when both values are integers, a problem remedied in Python 3:

>>> 1 / 2
0
>>> 1.0 / 2
0.5

Using 3.0 in the multiplication will make sure the left-hand operand of the division is a float.

You can also use from __future__ import division at the top of your script to switch to proper true division for the / operator where it always returns a float result.

Next, you are not using proper exponents in your formula; it is not size / (i + 1) ; it is size / (2 ** i) ; you need to divide by the powers of 2 here; not divide by 1, 2, 3, 4, but 1, 2, 4, 8, etc:

tot = 0
for i in range(tri):
    tot += 3.0 * size / 2 ** i

Now you get a result that matches Wolfram Alpha:

>>> tri, size = 8, 4
>>> tot = 0
>>> for i in range(tri):
...     tot += 3.0 * size / 2 ** i
... 
>>> tot
23.90625

Answer 2

Change:

float(size/i)

to:

float(size)/i

Answer 3

Due to the operator precedence in Python ;

size/i+0.0000001

uses integer division

size/i

then adds 0.0000001. Effectively, it's

(size/i)+0.0000001

Instead, use:

float(size)/i

to force floating point division.