geoboard triangle encloses dots

John E. Franklin · 2012-06-01 20:55:35

I have solved the geoboard triangle encloses dots
problem from an old algebra book I do not have
right now. I know my answer is different than the
books though as I recall the answer was much
simpler than my way. Does anyone know the
simpler answer from an old algebra book.

Basically it goes, on a geoboard or dots on graph paper
at every one unit in every direction, draw a random
triangle that uses these dots as corners. Now come
up with a formula or method to get how many dots
are enclosed in the triangle.

Since I've already got a method I just thought up, I
really just want to know if anyone can find this
answer somewhere on the web or in a book, so I can
try to find a connection between my complicated
method and their simple equation that always worked,
I recall from 2 years ago while studying with a friend
and her book.

John E. Franklin · 2012-06-01 22:01:09

The triangle dots on the perimeter are counted so it is inclusive in this way.
The interior dots if any are also counted. There is a fairly simple formula
for that gets the number of dots given any geoboard triangle, but my mehtod
is much harder as it makes a rectangle around the triangle and then
subtracts off the 3 right triangles, which I have a mehtod for which is not
really easy, because you have to find the number of dots on the hypotenuse
by finding prime factors in common between the vertical and horizonat runs or
legs of the right triangle. So the whole process is much harder than the answer
in the book I don't have, but may be able to get it if her relatives can find it as
she passed away a couple years ago, a dear friend of mine, and spectacular
at mathematics too with a masters in math.

Bob · 2012-06-01 23:12:00

hi John,

Can't find exactly that but this might give you a start:

http://mathforum.org/trscavo/geoboards/intro4.html

Bob

Math Is Fun Forum

#1 2012-06-01 20:55:35

geoboard triangle encloses dots

#2 2012-06-01 22:01:09

Re: geoboard triangle encloses dots

#3 2012-06-01 23:12:00

Re: geoboard triangle encloses dots

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