median
don steward
mathematics teaching 10 ~ 16
don steward
mathematics teaching 10 ~ 16
Sunday 31 October 2010
pythagoras plank
find the length of the plank (or long stick) in this right angled triangle
that just touches a 3m square, in the corner (as the diagram shows)
Friday 29 October 2010
pythagoras justification
when shapes are similar their areas are in proportion to the squares of corresponding sides
drop a perpendicular from the apex at the right angle to form two similar triangles (relatively straightforward to justify) which are similar to the original triangle
k(5^2) = k(4^2) + k(3^2)
and this generalises...
not that helpful as a means of justifying the theorem maybe, but a neat enough way of tying in the area property of similar shapes
[ from the website betterexplained ]
Sunday 24 October 2010
Saturday 23 October 2010
Wednesday 20 October 2010
number plus reciprocal
what is the smallest positive value that a number plus its reciprocal can have?
test this with decimals and fractions
trying to prove the result might involve rearranging an inequality
a number added to its reciprocal is 2.9, what is it?
a number added to its reciprocal is 2.05, what is it?
a number added to its reciprocal is 2.625, what is it?
test this with decimals and fractions
trying to prove the result might involve rearranging an inequality
a number added to its reciprocal is 2.9, what is it?
a number added to its reciprocal is 2.05, what is it?
a number added to its reciprocal is 2.625, what is it?
Saturday 9 October 2010
Penrose, kites and darts
Sunday 3 October 2010
trapezium property
construct any trapezium (a trapezoid in the US) and draw the two diagonals
at the point where the diagonals meet, construct a line parallel to the two parallel sides of the trapezium
what do you notice?
can you prove it?
this is an old problem, utilised in Michael de Villiers' admirable work on proof and geometry
use similar triangles to show that the length is the harmonic mean of 'a' and 'b'
at the point where the diagonals meet, construct a line parallel to the two parallel sides of the trapezium
what do you notice?
can you prove it?
this is an old problem, utilised in Michael de Villiers' admirable work on proof and geometry
use similar triangles to show that the length is the harmonic mean of 'a' and 'b'
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