A clarification in reply to some off-list discussion:
There is a proper use of the "halfway" language for a geometric mean, if one
speaks in logarithmic terms ==>
Let M be the geometric mean of the quantities Q1 and Q2 ==>
M = Sqrt(Q1*Q2). Then, taking the Log :
LogM = (1/2)*Log(Q1*Q2) ( freely choosing any logarithmic base), or
LogM = (LogQ1 + LogQ2)/2, ie, the Log of M is the arithmetic mean of the
Logs of Q1 and Q2, or, IOW ==>
The Log of the geometric mean of two quantities is the halfway point between
the Logs of the two quantities (using any logarithmic base).
-----Original Message-----
From: Bob Sciamanda
Sent: Friday, April 03, 2015 8:05 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Halfway point ???
My humble advice to teachers:
Please do NOT take away from this discussion (and teach) the idea that the
term "halfway" can be ascribed to the geometric mean of two quantities. IMHO
this would do extreme violence to any, however intuitively stretched,
legitimate meaning of the concept "halfway". The arithmetic mean of two
quantities IS the halfway point between these quantities. The geometric
mean is just the geometric mean - it has its uses, but it is NOT the halfway
point. Let us not return our language to BABEL.
-----Original Message-----
From: Bob Sciamanda
Sent: Friday, April 03, 2015 8:55 AM
To: PHYS-L
Subject: [Phys-L] Halfway point ???
Wimp.com posted this banner, with no explanation ==>
Today's Fun Fact: An average dust particle is the halfway point
between the size of the Earth and the size of a proton.
Can anyone discern a “thought process” which makes this statement meaningful
?
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
www.sciamanda.com
_______________________________________________
Forum for Physics Educators
Phys-l@www.phys-l.org http://www.phys-l.org/mailman/listinfo/phys-l
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
www.sciamanda.com