What's Quadrance?

Geometry Level 2

The side lengths will be represented as quadrance. Quadrance = Side Length Squared.

A right angle triangle has a quadrance of 8 and another quadrance of 7, what is the quadrance of the hypotenuse?

113 11 15 10

1 solution

Harrison Froats
Jun 9, 2017

To solve this triangle we must use pythagoras theorem, which is a^2+b^2=c^2. But because the side lengths are quadrances' the equation is simplified to a+b=c. Therefore the equation will look like 7+8=15.

Do you want the length of the hypotenuse or the square of the length of the hypotenuse?

Calvin Lin Staff - 3 years, 11 months ago

Try to use LaTeX in your solution, where necessary.

Peter Michael - 4 years ago

I'm going to be a little obtuse about this. He wants to use quadrance. See: Prof. N.J. Wildberger with regards to Rational Trigonometry.

Peter Michael - 3 years, 11 months ago

Can you clarify further?

The length of the hypotenuse is $\sqrt{ 15 }$ . The square of the length of the hypotenuse is $15$ .

The problem asks for "what is the length of the hypotenuse", and not "what is the square of the length of the hypotenuse".

He did start off by saying "The side lengths will be represented as quadrants.", but I do not fully understand the implication of that statement. IE if he says "the side length is 4", does it mean that "the actual side length is 4", or that the "represented quadrant is 4"?

Calvin Lin Staff - 3 years, 11 months ago

So yes, the wording of the question needs some work. And quadrant... while if you stretch the meaning, is close to what he is looking for. It is the quadrance of the line. As the quandrance of the line (as it is for any line) is distance squared. I will do my best to work on some problems, and a wiki page related to rational trigonometry ASAP. As hopefully, I will be able to do some justice to these ideas and concepts.

Peter Michael - 3 years, 11 months ago

@Peter Michael – Thanks for clarifying. I've made it "quadrant of the hypotenuse".

Calvin Lin Staff - 3 years, 11 months ago

@Calvin Lin – I think its supposed to be quadrance, if we are begin technical... but this is difficult to be technical about this when Wildberger is the one who came up with all of this. I really think you should take a look at his youtube lectures on it.

You guys would be really getting ahead of the curve if you got a Rational Trigonometry quiz/wiki/topic going. I suppose it does not just fall on the staff but the community as well.

Peter Michael - 3 years, 11 months ago

@Peter Michael – Thanks. I've updated the terminology in the problem.

Calvin Lin Staff - 3 years, 11 months ago

What's Quadrance?

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