Matbog.dk

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.

All right, all right. It's here, yay! Tomorrow is "Epic π-day".

My lack of enthusiasm is due to several errors in the meme going around:

1) Since π is irrational, it is not "equal to" any number with finitely many digits. The "=" should be a "≈".

2) The rounding is wrong. Since the next digit is a "5", one should round up, not down. So, 9:26:54, or even better: Somewhere in between those two, slightly closer to 9:26:54.

3) It only works if you write dates in the (highly non-standard) way that americans do. Month-day-year is so illogical it should be illegal. The ISO standard is YYYY-MM-DD. And it has the huge advantage that sorting dates alphabetically also sorts them chronologically.

But then again, we wouldn't have a pi-day if everyone followed the ISO standard.

Happy Pi-day, everyone! Please point out the above errors to anyone posting the meme, and raise mathematical awareness!

Just one day to go!

Yup.

And that point, right in the middle, where the Pringle appears to be perfectly horizontal is called a "saddle point" for a very good reason. :)

The "c" in the equation is actually almost redundant. The only effect is has is that when it's negative, it turns the Pringle upside-down. Everything else it does can also be achieved by changing the value of a and b.

Have a lovely day!

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:

---
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.
---

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! :)

This is probably inspired by the famous quote of Eugene Wigner:

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve".

It's the basic philosophy of MatBog: One should attempt to learn mathematics in the same way one learns a language. Not looking for "understanding" all the time, but rather see, hear, learn and use the words as much as possible. The understanding comes all by itself later on. :)

This one was not really fair. Sorry. :)

I'll post the "answer" in the comments below.

Nørd-test!

Hvis du forstår denne her, så er du en kæmpe nørd! -På den allermest positive måde, selvfølgelig!

Lad være med at afsløre det i kommentarerne. Tryk i stedet "share" hvis du forstår den. ;)

This is the wave equation.

I am posting it in case you are considering a tattoo. If you're looking for something to write permanently on your body which is short and simple, yet fascinating, deep and incredibly complex, forget about chinese letters or silly statements about life. This is it.

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.

(This is yet another post in English. There is a Danish translation in the first comment below.)

*Discusssion time*

This page is suddenly getting quite a lot of international visitors, thanks to Facebook-god, blessing us with a "like". Most of you are probably just passing by, deciding that a page for a danish math book is just a bit too weird. But others come back, and some of you have even "liked" us.

So my question is: Should this page aim to evolve into an international forum for intermediate-level (age group 15-20) math?

The original book, (matbog.dk) is, and will always be, a guide to the *danish* approach to learning math. It would not make sense to translate that into other languages.

But I don't see anything wrong with this page becoming a place where you can meet strangers from other countries with other curriculums, and be pleasantly surprised about how much math you still have in common.

I can keep posting danish translations of every post in the first comment.