# P = V * ( V / R ) = V2 / R

#### Jerramundi

##### Senior Member
Guess it just works, you get the same numbers when you run em through like Larry Fine pointed out.

And more praise to Whitney, that post should be a sticky in a math forum.
Look up "Order of Operations."
We learned the acronym "Please Excuse My Dear Aunt Sally." = Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

• Carultch

#### Jerramundi

##### Senior Member
Here's a basic list off mathematical properties/laws:
• Commutative Property of Multiplication
• Associative Property of Multiplication
• Multiplicative Identity Property
• Multiplicative Inverse Property
• Multiplicative Property of Zero
• Substitution Property
• Distributive Property
• Division Property
• Inverse Property of Inequality/Equality
There are more, but it's a good starting point.

#### electrofelon

##### Senior Member
@wwhitney hitting us with the actual mathematical rules and their names. Well done sir.
Pythagorean what?! It's the 3-4-5 rule!

I once corrected an elderly sparky I was working for, letting him know it's called the Pythagorean Theorem. He looked at me with so much hate in his eyes, lmfao  Pardon me for being picky, but making a right angle be forming a Pythagorean triple is technically the converse of the Pythagorean theorem (which is also true, even though converse statements are not generally true).

#### Carultch

##### Senior Member
What determines these rules? For me its always been difficult to memorize them since I don't know the how or why behind it.

Some mathematical rules are descriptive. Like the distributive property, the commutative property, and the associative property. These rules are determined first by recognizing patterns in mathematics, and second by stating a conjecture to generalize the pattern. Finally, the mathematician who discovers this rule will need to construct and publish a formal proof of the general case to show that it is true in all cases. If there are specific exceptions, those exceptions need to be identified as part of the statement of the rule. Specific examples do not prove rules no matter how many you evaluate, but one counterexample proves a rule to be false.

Other rules are prescriptive. Meaning they are true because we define them to be true. Order of operations is one example. In programming, it is called operator precedence. It is the convention of what operator takes priority over other operators. Prescriptive rules are determined as a consensus from patterns in the habits of other mathematicians in history.

The order of operations comes from what order of calculations come more frequently in application, than the alternative. Parenthesis and brackets are defined for overriding the default, so they have to come first. With exponents, it is much more common that you only intend to raise the previous number to the power, rather than everything before it. (-4)^2 ends up being the same thing as 4^2 and would be redundant if the minus is squared first. So if you write -4^2, you likely intend the answer to become negative. It would be a lot less convenient to write -(4^2) every time we intend the negative sign to be applied after the squaring. The motto to remember, "a minus ain't squared, unless it's been snared".

With the precedence between multiplication and addition, think of what you do when you add up cost of items on a bill. You first multiply each quantity with each unit cost, and then add up the line totals. It wouldn't make any sense to add up quantities of unrelated items, and then multiply that by a total of unit costs. It is much more common to multiply first, and then add, in applications of mathematics in general. A concept mathematicians call a dot product, which means multiply corresponding components and then add.

V^2/R

#### Jerramundi

##### Senior Member
making a right angle by forming a Pythagorean triple is technically the converse of the Pythagorean theorem
Ehh. I think I get what you're trying to say, but I think you're stretching.
3-4-5 IS certainly a Pythagorean Triple. That much I agree with.

But the "converse" of the Pythagorean Theorem (as defined in logic and mathematics) would be C^2 = A^2 + B^2.

I suppose you could make that argument if "The 3-4-5 Rule" was written as "The 5-4-3 Rule," but it isn't.

You could approach it that way and say you are "using the 'converse' of the Pythagorean Theorem," but "The 3-4-5 Rule" as written is much closer to the Pythagorean Theorem, typically expressed as A^2 + B^2 = C^2... than it is the "converse" of the Pythagorean Theorem, expressed as C^2 = A^2 + B^2.

#### electrofelon

##### Senior Member
Ehh. I think I get what you're trying to say, but I think you're stretching.

3-4-5 IS certainly a Pythagorean Triple. That much I agree with.

But the "converse" of the Pythagorean Theorem (as defined in logic and mathematics) would be C^2 = A^2 + B^2.

I suppose you could make that argument if "The 3-4-5 Rule" was written as "The 5-4-3 Rule," but it isn't.
You could approach it that way and say you are "using the 'converse' of the Pythagorean Theorem," but it's not how the rule is typically written.

The Pythagorean theorem states (a little crudely but you know what I mean) that in a right triangle, a^2+b^2=c^2
Now given a statement like that, you can NOT assume the converse is true, that is "IF I have lengths where a^2+b^2=c^2, then I have a 90 degree angle." The converse does always hold for the Pythagorean theorem, but not generally in mathematics.

#### LarryFine

##### Master Electrician Electric Contractor Richmond VA
Factoid: In The Wizard of Oz, Scarecrow misspoke when he was showing off his new brain.

He referred to an isosceles triangle instead of a right triangle when quoting the formula.

• Jerramundi

#### Jerramundi

##### Senior Member
Factoid: In The Wizard of Oz, Scarecrow misspoke when he was showing off his new brain.

He referred to an isosceles triangle instead of a right triangle when quoting the formula.
That's because the Wizard hustled his a\$\$, lol.

#### LarryFine

##### Master Electrician Electric Contractor Richmond VA
That's because the Wizard hustled his a\$\$, lol.
You mean he got a defective brain? • • Jerramundi and Carultch

#### GoldDigger

##### Moderator
Staff member
Pardon me for being picky, but making a right angle be forming a Pythagorean triple is technically the converse of the Pythagorean theorem (which is also true, even though converse statements are not generally true).
Correct. Set up as a proposition what we generally call the Pythagorean Theorem states that IF ABC is a right triangle, with the right angle at C, THEN labelling the lengths of the sides opposite each point a, b, and c, a**2 + b**2 = c**2.
Going a little farther into the geometry, which is not usually done, we find that rather than a simple IF-THEN we have an IF AND ONLY IF-THEN. Thus the converse is true.
A great example of people casually misusing logic and coming out with the right answer anyway.

#### Carultch

##### Senior Member

The Pythagorean theorem states (a little crudely but you know what I mean) that in a right triangle, a^2+b^2=c^2
Now given a statement like that, you can NOT assume the converse is true, that is "IF I have lengths where a^2+b^2=c^2, then I have a 90 degree angle." The converse does always hold for the Pythagorean theorem, but not generally in mathematics.

There's another theorem that allows you to close the loop on the converse of the Pythagorean theorem, used in this manner. The converse of the Pythagorean theorem turns out to always be true, because it is a consequence of another theorem about triangles.

There are congruence theorems of triangles, based on if you know whether sides and angles are congruent, and the order in which they are specified. Congruent means that you can mirror, rotate, and translate the triangles, to make them identical. The theorems for triangle congruence are SAS, ASA, AAS, SSS, and HL. S=side, A=angle, H=hypotenuse, and L=leg. There is no ASS theorem of congruence. An example of why, is that given A=30 degrees, S1=8in, and S2=5 in. Draw it to scale, and you'll see that there are two different triangles that can be created from these constraints.

The example of using a known Pythagorean triplet to conclude it is a right triangle. The SSS congruence theorem states that given all three side lengths of a triangle, you have defined the triangle to congruence with all other triangles of the same three side lengths. Given 3, 4, and 5, as the side lengths, you cannot create a triangle that is not a right triangle. At least in standard Euclidean space.

#### Carultch

##### Senior Member
Factoid: In The Wizard of Oz, Scarecrow misspoke when he was showing off his new brain.

He referred to an isosceles triangle instead of a right triangle when quoting the formula.

He misspoke in two different ways. #1, it's the fact that it is a right triangle that matters for that equation, and whether it is isosceles is irrelevant, #2, it's squares in reality and not square roots as he says in the line. I don't believe it is even possible to make sqrt(a) + sqrt(b) = sqrt(c) for any triangle.

I don't know whether this was intentional as his scripted line, or it was a mistake on the actor's part that the director decided to keep anyway. Either way, it fits the whole idea of that scene for the Wizard to be an illusionist without any real power. He's either giving the characters something they already had, or giving them a symbol of what they seek.

#### oldsparky52

##### Senior Member
Some of this is starting to sound like Bill Clinton
It depends upon what the meaning of the word 'is' is.

• Carultch

##### Senior Member
You mean he got a defective brain? "So, who's brain did you get?
Abby...Abby Normal!"

#### mbrooke

##### Batteries Included
No, you may be thinking of this:

a * (b + c) = (a * b) + (a * c ) (distributive law of multiplication)

The parentheses on the right hand side are usually omitted, as it is understood that you group multiplication operations together before doing addition operations.

With multiplications only, the order doesn't matter:

a * b = b * a (commutative law)
a * (b * c) = (a * b) * c (associative law)

And so again, when multiplying more than two numbers, the parentheses are usually omitted, because both options give the same result.

Division throws a wrench into things, order starts to matter. I think of division as "take the reciprocal and then multiply". So if you make that explicit (using Recip(a) to mean 1/a, the reciprocal of a) and keep track of which number get the reciprocal, it all works out:

a * (b / c ) = a * (b * Recip(c)) = (a * b) * Recip(c) = (a * b) / c

Because of the above, it's safe to write a * b / c, there's no ambiguity. But something like a * b / c * d should be avoided, as it is not clear if you mean a * (b / c) * d or a * b / (c * d), which are different.

Lastly, Recip(b * d) = Recip(b) * Recip(d), so you have the general rule for multiplying two fractions of "multiply the numerators and multiply the denominators":

(a / b ) * (c / d) = a * Recip(b) * c * Recip(d) = a * c * Recip(b) * Recip (d) = a * c * Recip(b * d) = (a * c) / (b * d)

Wayne

Alright, it makes sense half way... But going by this, why would I fail a math test for saying (V*V)/(R*R)? I see the concept in your last half, but still don't "get" it.

#### oldsparky52

##### Senior Member
Alright, it makes sense half way... But going by this, why would I fail a math test for saying (V*V)/(R*R)? I see the concept in your last half, but still don't "get" it.
From Wayne, a * (b / c ) = a * (b * Recip(c)) = (a * b) * Recip(c) = (a * b) / c

Original problem V*(V/R)

So, following what Wayne put out, V*(V/R) = V*(V*1/R) = (V*V)*1/R = V*V/R = V²/R

For me it was always easiest to look at it like I posted in #15. Consider the (V/R) as a fraction and consider V a fraction also (V/1) then multiply the fractions.

• mbrooke and Carultch

#### Carultch

##### Senior Member
Alright, it makes sense half way... But going by this, why would I fail a math test for saying (V*V)/(R*R)? I see the concept in your last half, but still don't "get" it.

Because you would be inserting an extra 1/R in the equation that wasn't there in the first place.

• Jerramundi

#### Hv&Lv

##### Senior Member
Is P = V * ( V / R ) the same as V2 / R ? Why? And if not which is correct? .....................................
I didn’t go through and read all the posts.
So if it’s done already, sorry.

Let V = 4
Let R = 2

so V*(V/R) =
4*(4/2)
4*(2)
8

now the other one.
V^2/R
(4*4)/2
(16)/2
8