In his 1947 book, One, Two, Three...Infinity,
physicist George Gamow poses a pirate treasure problem that has since become a classic. Below is my reworded statement of the puzzle.
Among a pirate's belongings you find the following note:
The island where I buried my treasure contains a single palm tree. Find the tree. From the palm tree, … Continue Reading ››
Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other.
Believe it or not, you can stick a pin straight through both maps … Continue Reading ››
A recent post on the my NCTM discussion group
asked about tools to help students visualize and understand addition and subtraction of integers.
I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … Continue Reading ››
The picture below on the left shows a right triangle JML
with altitude KM
. This altitude is defined as the geometric mean
. Using similar triangles, you can prove that JK
². Another way to think about this construction is shown below on the right. Start with segments JK
and … Continue Reading ››
Twitter is a great place to find geometry problems. The July 22, 2017 post of xylem
presented the image below with two squares, ABCD
sharing a vertex. Given that AE
= 5, what is the length of DG?
My first thought was that surely the problem was … Continue Reading ››
In the interactive websketch below (and here
on its own page), ABCD
is an arbitrary quadrilateral whose midpoints form quadrilateral EFGH
. Drag any vertex of ABCD
. What do you notice about EFGH
The midpoint quadrilateral theorem, attributed to the French mathematician Pierre Varignon, is relatively new in the canon of geometry theorems, dating to 1731. Mathematics educator Chris Pritchard … Continue Reading ››