My daughter's nursery is currently decorated with a La Linea cartoon, which leaves a lot of space.

I'd like to put up some useful equations so that she can become familiar with them. Wallpaper would not really be suitable as the equations would repeat all the time, so I think transparent stickers
would be better.

As this product doesn't exist, I'm painting them on. So far I have decided on the proof of Pythagorean theorem, the Golden Ratio of a pentagon/pentagram (which will make us look like Wiccans), a chaos theory graph and some chemical reactions.

Diagrams is better than equations (seems to be your opinion,
too). How about Cantor's diagonal proof for the existence of
an uncountable infinity?

It'd be a real achievement if you could get your daughter
comfortable -- while still young and mentally flexible -- with
concepts like infinity, that give adults difficulty.

I've tried it and it doesn't work. Well, not with my daughter. Not sure about [eleventeenthly]. He's comfortable with uncountable and countable infinities because we've talked about them since he was about four. My daughter watched an OU programme on the Hilbert Hotel back in the 'nineties and was keen but hates mathematics.

I think talking works better than visual for these children. They're all different of course.

//Planck's constant, though- it's not big, and it's not clever.//
But it is nu. (Well actually it's h, but it is inversely proportional to nu. So maybe it's old.)

Add some fractals if you have the time. Or add a graph of the fishpond
equation, which is beautiful and simple.

Also, e-to-the-i-pi = -1 (looks prettier with superscripts).

Also also, there is a beautiful graphic proof to do with sines and slopes and
gravity. It shows a triangular wedge (3:4:5, I think, and flat on the bottom)
around which is looped a series of balls linked by string. It's self-evident that
the chain of balls doesn't spontaneously turn, which proves that the force
imposed by the 5 balls on the long sloping side is exactly balanced by the force
imposed by the 3 balls on the short vertical side. It's on some mathematicians
headstone, somewhere.

Also, you HAVE to have a number line with the primes marked out. Primes are
everything.

Feynman diagrams are cute too.

Ooooh! I just thought of something relating to primes. It doesn't really fit
here, though.

[MaxwellBuchanan] The golden ratio is pretty
much the basis of fractals, so that's covered
(pentagon/pentagran).

Primes and then perfect squares, Pythagorean
triples, the Fibonacci sequence and stuff I think
will be things that go round the wall at waist level,
like the alphabet (below La Linea's line of course).

[8th of 7] It's not the length of your Planck, but
the chasm you span it with*.

Disclaimer: I'm drunk now and typing between
hiccups.

I don’t remember ever voluntarily deciding to use an
equation in my life. They’re pointless, annoying,
indecipherable and only exist for effect and showing
off to other people, a bit like latin. Use of equations
should be seen as a detectable early sign of
antisocial mental abnormality.

[IT] Ever ridden in a plane, train, automobile, used a
computer, crossed a bridge, etc., etc.? If so you've
used quite a few equations, if only at one remove.

Wrong. I must have cheated and did it the easy way, as not
once have I ever used an equation to do any of those
things. If it were mandatory, I wouldn't have bothered of
course.

I generally use Latin so i don't accidentally kill people by giving them something poisonous, contraindicated for them, or lead them to overdose. Equations are similar in that they allow people to do trivial things like design aircraft which don't fall out of the sky unexpectedly or buildings which don't fall over and crush all the occupants to death. People have this irrational desire not to die in agony for some reason. Can't think what that's about.

It’s entirely illogical. The from the point that you’re
dead onwards, there’s going to be no way of
handling pain stimulus, nor any way of formulating a
memory of the prior pain, so it really doesn’t matter
how painful the death was once you’re dead. In fact,
nothing really matters. Given that we’re all going to
die, nothing really matters while we’re alive either.

Yes, French would be ideal for that purpose.
[Ian], i'm definitely on the same frequency as you there but i have no idea how to describe the waveform to you.

//I generally use Latin so i don't accidentally kill people//
Understood. Paradoxically, where I am, Latin* is prohibited
for exactly that reason: things like "qid" "qd" & "po" are
verboten, because of the potential for misunderstanding.

*well, Latin initialisms, anyway. But if someone wrote "per
os," the problem would be non- rather than mis-
understanding.

I think Frank Gilbreth, in the _Cheaper_By_The_Dozen_ book, did something like this. (But maybe he had the decency to wait until the kids were out of the nursery.)

[Mouseposture], the Institute insists we write our Rx in Latin. It would be problematic with them if they found out we didn't and other herbalists wouldn't understand us unless they knew English. I think the answer to that is to abandon English as the medium for communication in schools and universities.

//The golden ratio is pretty much the basis of fractals//
?
On the other hand, the golden ratio IS the basis for the Fibonacci sequence (basis? well, they're intimately inter-related). It's quite fascinating that an equation primarily using an irrational number can give whole-number results.

The only one that people SHOULD learn is the Rule of
78 (The one to calculate interest/principal ratios in
loan repayments). It's desperately misunderstood by
the great majority of people, who are held in
financial servitude by banks and employers as a result
of their ignorance.

That’s ridiculous. It’s like when people say “less is
more”. No it isn’t. Don’t they realise, that less by
definition is less than more, therefore also, more
is more than less. Hence, less is less. Or more is
more. Not the other way round.

Also, when people say “the journey is the
reward”. Utter stupidity. When I want to go
somewhere, or have to go somewhere, it’s
because I want to get there. I didn’t want to take
the journey, I wanted to get to the destination.
The only reward involved with the journey is being
thankful I don’t live on the Northern Line.

That may be true, [Ian Tindale], but you still live near
the end of that god-awful Docklands line, out with
the muggers, toerags and TV thriller camera crews
spend the day shooting each other, shooting up and
shooting shooting scenes.

I was going to do something like this once we had our first. I would paint pictures that had noticeable patterns, some basic XY graph-inspired pictures, things that would mean something inspiring and mathematical to a young mind that didn't quite grasp equations yet.

Go for Escher pictures, anything that has a superset repeating transitional pattern. Choose good pictures that are like good music in their relation to mathematics.

Add some of that chalkboard paint. Add hidden features that the child can discover on their own.

Perhaps a tree with branches that divide evenly, repeatably, like a fractal pattern.

Don't try to go too many different directions with it. The main purpose is to inspire in a direction.

A number line is in definite order.

But also bring in pictures of the physical world that clearly have some relation to the math subtly presented. A suspension bridge picture, perhaps.

The best gag is to put up one of those" learn the letters" charts-
A is for apple, B is for bee, C is for cat … but give them a french
one, where P is for Pomme, C is for Chien, M is for Maison …

"A is for aitch ... C is for ctenophore D is for
djinn E is for eff F is forgotten G is for
gneiss ... K is for knitting L for
leather M is for mnemonic O is for owe P is for
psychiatry .... T is for tsar ... W is for
writing X is for xenon Y is for ytterbium Z is for
later."

As mentioned I'd start with the laws of motion, then
gravity. The one not mentioned is Kepler's laws as
they have good associated graphics. Particle
mechanics, Maxwell's equations, SOHCAHTOA, basic
integrals and thermodynamics.
I've thought about this a lot as our next child may be
a boy, so I'd get to design the room. My wife
suggested a Wall-E theme, but I thought I could slide
in some real science in the design.

[Daseva] as fr as I know, he never actually built the
illustrated device. The picture alone is enough - it's clear
from the picture that the loop will not spontaneously rotate
round and round - it'll just hang there. That in turn proves
that the forces on both slopes are balanced. So, it was the
perfect gedankenen experiment.

//it's clear from the picture that the loop will not spontaneously rotate round and round// Plenty of perpetual motionists would disagree vehemently with this assessment.

Good idea --- but leave infinity out until it is observed and good luck with that. All mathematical proofs are meaningless without confirmation by an observer.

Unless you can somehow indicate that in the abscence of reality maths is just fantasy. Perhaps thats why there is no prize for maths...

You can't forget Reimann, or Fourier, or you could do the Navier Stokes thing, which as I understand is really infinitely long (so choose as many terms as you like to make a nice wrap around)...