Monthly Archives: March 2015

An almost real life geometry problem

I needed to move a point around a circle, in a computer graphics application, using the mouse pointer. It is clearly not sensible to have mouse pointer on the point all the time, so the problem was

“For a point anywhere, where is the point both on the circle and on the radial line?”

point on circle 2

It may help to see the situation without the coordinate grid on show:

point on circle 1

This is a problem with many ways to a solution, some of them incredibly messy !

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Filed under engineering, geometry, math, teaching

She Wants Us to Study for Math

For those of you who don’t know “Math with Bad Drawings” this is a real treat.

Math with Bad Drawings

Our teacher’s gone utterly crazy.
No one can fathom her wrath.
She wants us to do the impossible:
She wants us to study for math.

20150324074539_00001

How can you study for something
where talent is so black-and-white?
You get it, or don’t.
You’ll pass, or you won’t.
It’s pointless to put up a fight.

Her mind must have leaked out, like water,
and slipped down the drain of the bath.
I might as well “read up on breathing”
as study for something like math.

Math’s an implacable tyrant,
a game that I never can win.
And even if I stood a prayer of success,
how would I even begin?

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My teacher, the madwoman, told me:
First, list the things that you know.
Her mind’s gone to rot.
Still, I’ll give it a shot,
though I’m sure that there’s nothing to—

oh!

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School——>PARCC tweet———>suspension———->and then?????

Thank you Audrey Watters for leading me to this exposure of the behaviour of testing corporations.

These two are MUST READs, and should be passed on to everybody:

http://www.bobbraunsledger.com/breaking-pearson-nj-spying-on-social-media-of-students-taking-parcc-tests/

http://kengreenwood.com/pearson_spying_on_kids/

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Filed under big brother, education, testing

A fun math/computing problem

I found this on http://www.playwithyourmath.com/ and adapted it a little.

The number 25 can be broken up in many ways, like 1+4+4+7+9

Let’s multiply the parts together,  getting 504 (or something near)

Problem 1: Find the break-up which gives the max product of the parts. 1+1+1+…+1 is not much use.

Problem 2: Find a rule for doing this for any whole number.

Problem 3: Put this rule in the form of a computer algorithm (pseudocode is OK)

Problem 4: Write the rule as a single calculation (formula)

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Filed under algebra, math, operations

Egyptian fractions

I found this on Quora. What would the standard algorithm be, I wonder.
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David JoyceDavid Joyce, Professor of Mathematics at Clark Uni… (more)

Suppose you have five loaves of bread and you want to divide them evenly among seven people.  You could cut the five loaves in thirds, then you’d have 15 thirds.  Give two of them to each of the seven people.  You’ll have one third of a loaf left.  Cut it into seven equal slices and give one to each person.

\frac57=\frac13+\frac13+\frac1{21}
There may be other solutions.   a = b = 3, c = 21.   (Egyptian Fractions)

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Filed under arithmetic, fractions, math, operations

Fractional doggerel – verse problem

Mary’s mother brought a pizza
For her little kiddies, two.
“Johnny, you can have threequarters.
Mary, just a half will do.”.

Then the kiddies started eating.
Soon Mary grabbed her final piece.
“That’s mine” screamed Johnny, then the fighting
Broke the tranquil mealtime peace.

How much pizza then was eaten?
How much pizza on the floor?
Mother swore and left the building.
“I should have ordered just one more”.

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Filed under arithmetic, fractions, humor, language in math, verse