The teacher said "If you join the midpoints of the sides of an irregular quadrilateral you will always get …". Before the teacher could finish this statement four students guessed what the next words could be.
Arun guessed ‘a square’, Bronwyn guessed ‘a parallelogram’, Colin guessed ‘a rectangle’ and Doreen guessed ‘another quadrilateral similar to the original’. Who was right? Justify your answer.
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Bronwyn was correct. It is possible to prove this fact using vectors.
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Numbers and the Making of Us
I initially heard this book described on the Grammar Girl podcast and immediately went to find out more about it. I now have it on my Christmas present wish list and am looking forward to receiving a copy (hint!).
"Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists." more...