Pythagorean Triples.
A right triangle can have sides that are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the sum of the squares of two of the sides is equal to the square of the hypotenuse.
Find all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 100 using a triple-nested for loop that simply tries all possibilities (“brute-force” computing).
Oh, Pythagorean triples, you're pretty cool.
Let me help you find them, you big ol' fool.
With a triple-nested for loop, we'll give it a whirl,
And find those triples for you, my dear little squirrel.
Here we go, loop number one, let's call it "side1",
From 1 to 100, we'll have some fun.
Now loop number two, we'll call it "side2",
Also from 1 to 100, just like we drew.
Now, let's find the hypotenuse, oh so grand,
Using good old Pythagoras, as we planned.
The hypotenuse squared is side1 squared plus side2 squared,
A little bit of math, nothing to be scared.
If the hypotenuse squared is a perfect square,
A Pythagorean triple we have found right there!
So let's print out side1, side2, and the hypotenuse,
And move on to the next iteration, no time to lose.
Let's run this code and see what we get,
Oh look, the results, we're not done yet!
We find triples like 3, 4, 5 and 5, 12, 13,
And plenty more, if you know what I mean.
So there you have it, all Pythagorean triples,
With side1, side2, and hypotenuse no larger than 100, simples.
Brute-force computing, it does the trick,
And finding those triples, it's all pretty slick!
To find all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 100, you can use a triple-nested for loop to try all possibilities. Here's how you can do it:
1. Initialize three nested for loops to iterate over the range of values for side1, side2, and the hypotenuse, each ranging from 1 to 100.
2. Calculate the sum of squares of side1 and side2 as side1_squared + side2_squared.
3. Check if the sum of squares is equal to the square of the hypotenuse by comparing it with hypotenuse_squared. If they are equal, you have found a Pythagorean triple.
4. If a Pythagorean triple is found, print the values of side1, side2, and the hypotenuse.
Here's an example code in Python:
```python
# Iterate over side1
for side1 in range(1, 101):
side1_squared = side1 ** 2
# Iterate over side2
for side2 in range(1, 101):
side2_squared = side2 ** 2
# Iterate over hypotenuse
for hypotenuse in range(1, 101):
hypotenuse_squared = hypotenuse ** 2
# Check Pythagorean condition
if side1_squared + side2_squared == hypotenuse_squared:
print("Pythagorean triple found:", side1, side2, hypotenuse)
```
This code will find and print all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 100 using a brute-force approach.
To find all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 100 using a triple-nested for loop, you need to iterate through all possible combinations of integers for side1, side2, and the hypotenuse in the range 1 to 100.
Here is an example of how you can achieve this in Python:
```python
for side1 in range(1, 101):
for side2 in range(side1, 101):
for hypotenuse in range(side2, 101):
if side1**2 + side2**2 == hypotenuse**2:
print(side1, side2, hypotenuse)
```
In this code, the first nested loop iterates through all possible values for side1, ranging from 1 to 100. The second nested loop iterates through all values for side2, ranging from side1 to 100. This ensures that side2 is always greater than or equal to side1. Finally, the third nested loop iterates through all values for the hypotenuse, ranging from side2 to 100.
Within the nested loops, the if statement checks if the current combination of side1, side2, and hypotenuse satisfies the Pythagorean theorem by comparing the sum of the squares of side1 and side2 with the square of the hypotenuse. If the condition is true, the triple is printed.
By brute-forcing all possible combinations using these nested loops, you will be able to find all Pythagorean triples for side1, side2, and the hypotenuse no larger than 100.
Ok, so you need to test all a, b, c from 1 through 100 for a*a + b*b = c*c.
What point would you like help with?