Let's say that we want to build a frame. As we layout the metal, how do we ensure it is square? There are several ways, one is to use the right angle calculations that you learned in an earlier chapter. The second is to use Pythagorean theorem that states: the squares of each of the shorter lengths, added together, gives you the square of the hypotenuse (longest leg of the triangle). Mathematically, this is expressed as

Question

Let's say that we want to build a frame.  As we layout the metal, how do we ensure it is square?  There are several ways, one is to use the right angle calculations that you learned in an earlier chapter.  The second is to use Pythagorean theorem that states: the squares of each of the shorter lengths, added together, gives you the square of the hypotenuse (longest leg of the triangle).  Mathematically, this is expressed as

In the Pythagorean theorem solution, the c2  is the corner to corner measurement.

However, there is an easier way, by using the 3 - 4 - 5 ratio.  So given the dimensions of 18" and 24" what would be the hypotenuse?

A hint: 18/3 is 6.

Extra credit if you tell me the difference between a 'theorem' and a 'law' in science.

GPT 3.5 · Answer

To ensure that the frame is square, we can use the 3-4-5 ratio. According to this ratio, if we have two sides measuring 3 units and 4 units, then the hypotenuse will measure 5 units.

Given the dimensions of 18" and 24", we can use this ratio.

18/3 = 6
24/3 = 8

So, the hypotenuse would be 6 * 5 = 30".

Now, let's discuss the difference between a 'theorem' and a 'law' in science:

- A theorem is a statement or principle that has been proven or demonstrated to be true using logical reasoning, deduction, or mathematical proofs. Theorems are specific to the particular field or subject they relate to, such as geometry or physics. They are derived from axioms, definitions, and established principles within that field.

- On the other hand, a law in science is a descriptive statement or equation that has been experimentally observed to hold true under certain conditions or in certain situations. Scientific laws summarize the regularities or patterns observed in nature and are often expressed in mathematical terms. Unlike theorems, laws do not require formal proofs and may not have a deep underlying explanation.

In summary, the main difference between a theorem and a law is the process of validation. Theorems are proven through logical reasoning or mathematical proofs, while laws are derived from empirical observations and do not necessarily require formal proof.