3blue1brownA Young Person's Guide to the Triangle of Power
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Tags: triangle-of-power
If you are reviewing entries for SoME, you have probably heard of the triangle of power. This is an attempt to introduce the concept to students who have not yet encountered logarithms. The tone is intended to be humorous, but it likely doesn’t work for the target readership. I hope you enjoy it.
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Way too long and unfocused for such a simple concept. And, in the end, triangle notation has no real practical use. Would have loved to see more of an angle at how the power rules can be taught better using ideas from the triangle approach.
The text is clear and easy to follow. It is written in a way that requires knowledge of the existing notation. I have come across this suggestion before. I see the following issues with the proposal:
Powers can be taught with the definition, the superscript states how many time to multiply the base. Then apply the definition in both directions to recover all of the rules. This proposal would require the triangle to be drawn throughout this process with a promise it will be useful later.
The log notation is typical function notation with the property a power can move to a multiplication. After obtaining this definition all of the log rules can be obtained with the aid of the index laws.
It is not clear how the triangle notation would work as well on the following:
x^ax^b=x^(a+b) ln(x^ax^b)=ln(x^(a+b)) Need to know how applying log to both sides is implemented in triangle notation ln(x^ax^b)=(a+b)ln(x) Need to know how to move the power of sub-triangle to a multiplication ln(x^ax^b)=aln(x)+bln(x) ln(x^ax^b)=ln(x^a)+ln(x^b) ln(AB)=ln(A)+ln(B) Is it going to be easy to verify the substitution to get the rule?
Also how do I write the triangle notation on a computer so it can be directly compared?
as an old, i enjoyed the humour and brevity