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Måske den sjoveste ligning i verden?

Denne ligning har 2 reelle løsninger. Kan du finde dem? Kan din matematiklærer finde dem?

Hvis du bruger et computerprogram til at løse ligninger, så er denne her ligning et fantastisk eksempel på hvorfor dette kan være en meget dårlig strategi.

Percentages. My old friend! You're back to bother me.

A Facebook friend of mine just asked for some "math help" on his wall. He needed to know "how to express the difference between 1.5% and 0.14% as a percentage?"

Specifically, he wanted "to know how much lower as a percentage 0.14% is than 1.5%"

So, I explained to him that the question could be understood in two ways, because the two numbers that were compared were percentages (hopefully of the same thing) themselves.

So, I explained that you could reach either the answer "1.36% ("points") smaller", or the answer "about 91% smaller", depending on how you read the question.

I also added that it was probably the latter answer he wanted, giving an example where the numbers 0.14% and 1.5% were error rates on a production of, say, 1000 teddy bears. In that case you were definitely interested in saying that the number of defect teddies had dropped by a whopping 91%.

And THEN came all his other facebook friends and added friendly "help" and "suggestions".

The latest addition to the "debate" is this one:

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I would agree that an undefined number times 2 = twice whatever number it was, originally, but being it's "undefined", we have no way of knowing its original "worth", nor what its "doubled worth" is, after multiplying it.
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Shall we just make it illegal to talk about percentages RIGHT NOW, PLEASE?

Get your coloured pencils out! Here's a challenge:

You have to colour the entire two dimensional plane. Yes, every point.

Ok, at least in theory, since you'd never finish in reality.

But here's the twist: Two points are not allowed to have the same colour if the distance between them is equal to one.

So, if you make one point green, then each point on the circle with radius 1, centered in that point must have a colour that isn't green.

Now, how many different colours do you need?

As always, look in the comments for ... well, not exactly an answer, but some hints. :)

One of my previous students was kind enough to post this on my wall.

So, I had to come up with a response... You can see the result in the comments.

These wishes are extended to all of you, of course! :)

Percentages: How do YOU feel about them?

Personally, I *hate* them!

If I was ever given the chance to pick one single concept in math, and make it go away forever, this would be it.

Here is an exercise to illustrate ONE of the reasons I hate them.

Two students (let's call them A and B) practise math seperately by finding exercises on the internet and answering them. Let's assume that every exercise is equally hard.

They both keep track of how many exercises they have done, and how many they have answered correctly.

Over the autumn, A gets 20% correct, and B gets 40% correct.
Over the spring, A gets 50% correct, and B gets 90% correct.

Now, over the whole year, who do you think has the best percentage score? A or B?

Look in the comments below for the (surprising?) answer. And as always: Look in the first comment for a Danish translation.