
The Mathematical Surprises of Triangles, Squares and Pentagons - sohkamyung
http://blogs.scientificamerican.com/guest-blog/martin-gardner-at-101-it-s-as-not-so-easy-as-3-4-5/
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SteveWatson
“Given a triangle with one obtuse angle, is it possible to cut the triangle
into smaller triangles, all of them acute?”

Isn't the answer obviously 'yes'? Am I missing something?

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3JPLW
It is possible, but I wouldn't consider it trivial. Given an obtuse triangle
with vertices A, B, and C, where vertex C is the obtuse angle, one of the
dissection lines _must_ split vertex C in order to make two acute angles.

Now, you have some choices as to where this line goes. If it is simply
dissected straight across to the line segment AB, then you can either form two
right triangles, or one acute and one obtuse. Either way, you're right back
where you started, needing to segment a non-acute triangle into acutes. So
that can't be the solution.

This means that the new segment starting from C must terminate at a new point
D in the interior of the triangle...

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pavel_lishin
> In another devious brainteaser, Martin displayed the following dissection of
> a triamond into four congruent convex pieces and asked for a dissection of a
> square using five congruent convex pieces.

> The answer, in hindsight, is blindingly obvious—did we mention that Martin
> was also an ace magician, and hence a master of misdirection?

I really want to know the answer, but Google isn't being helpful.

~~~
toth
Five stacked rectangles (height 1/5 of squares, width same as square).

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pavel_lishin
Damn. That _is_ blindingly obvious.

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sohkamyung
What really caught my eye in the article was the end: Martin Gardner's "The
Annotated Alice" has been updated yet again, this time for the 150th
anniversary of the story.

I have the previous two editions of the book and I'm seriously thinking of
getting this one too.

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yuchi
In the article there’s a statement that looks terribly ‘wrong’ for me:

> Jennifer McLoud, a Native American and the first in her family to earn even
> a bachelor's degree […]

Wait, was that somehow important? It feels so damn racist to me.

Small note, I’m italian and I’m honestly interested on how others see this.

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BB_T_WINSTON
I'll preface by saying that it certainly isn't relevant to the article, and I
do find the phrasing to be a bit demeaning to bachelor's degrees.

On the other hand, even going for a bachelor's degree can be met with a lot of
resistance in some family cultures. I've known families that ostracized a
member for being the first to go to college instead of pursuing the union or
the force. I can't speak to how widespread this is, but being the first to
make it to college is in itself sometimes a real achievement. It might be a
wild thought for those of us who were raised thinking a Bachelor's is just
part of the natural progression.

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xlm1717
Conversely, in some minority groups it can be a great source of pride to be
the first one in the family to go to college and get a bachelor's degree.

I don't think it's likely for the writer of the article to know that Jennifer
McLoud was the first in her family to graduate college without McLoud
revealing it herself. Automatically assuming it's racist seems like a stretch
and unnecessary.

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mc32
Agreed. Most of the time, perhaps all, I've heard this phrase, it's a source
of pride.

We have to remember, the US was vastly and primarily agricultural and largely
didn't attend secondary education in numbers till after WWII with the gi bill
and subsequent popularization of secondary education.

The phrase is typically a way to show achievement in the face of slim odds,
like from broken home, no tradition of emphasis on education, etc.

The only "racist" element, if it can be called that is the presumption the
secondary education is seen as modern sophisticated and good, which I think it
is, to practical extents, but can see where some may disagree.

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AnimalMuppet
One nit for your comment: In the US, "primary education" means grade school.
"Secondary" means high school. "Post-secondary" is college. Through WWII, the
majority of US children attended secondary education (high school) but not
college.

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mc32
True, it gets confusing, but tertiary to my mind means postgrad. But yeah, I
meant college/university was rare before the post war period. And people
thought and still consider it an achievement meriting praise.

