I think this is an interesting book. It uses visuals to prove various things, in algebra, geometry, trig, etc. There is a nice visual proof of why the geometric mean is less than the arithmetic mean, for example.
I looked at the proofs for Pythagorean theorem. Not obvious to me how the various dissections works, and I doubt that students will figure them out either. The dissections are nice, but you do need statements and reasons to justify the various things going on.
i love this stuff. haven't seen the book but many of 'em will presumably have appeared in MAA's _american_mathematical_monthly_ (which i used to see regularly).
i've been doing "lectures without words" in zine form (and distributing them in the low dozens) for, what, the better part of a year or so.
the "dissection" here (early on, in black-and-white), for me, qualifies as "without words" (and as a "proof from the book" per pal erdos). my first exposure to proof-by-dissection, though, was the far-less-obvious BEHOLD proof attributed to bhaskara. i saw it in the justly-famous dolciani series of highschool texts.
I think this is an interesting book. It uses visuals to prove various things, in algebra, geometry, trig, etc. There is a nice visual proof of why the geometric mean is less than the arithmetic mean, for example.
ReplyDeleteI looked at the proofs for Pythagorean theorem. Not obvious to me how the various dissections works, and I doubt that students will figure them out either. The dissections are nice, but you do need statements and reasons to justify the various things going on.
ReplyDeletei love this stuff.
ReplyDeletehaven't seen the book but
many of 'em will presumably
have appeared in MAA's
_american_mathematical_monthly_
(which i used to see regularly).
i've been doing "lectures without
words" in zine form (and distributing
them in the low dozens) for, what,
the better part of a year or so.
the "dissection" here
(early on, in black-and-white),
for me, qualifies as "without words"
(and as a "proof from the book"
per pal erdos). my first exposure
to proof-by-dissection, though,
was the far-less-obvious BEHOLD
proof attributed to bhaskara.
i saw it in the justly-famous
dolciani series of highschool texts.
owen thomas