Some easy unsolved math problems (High school grade)

Atran

Hi, I'm currently studying in high school. What I often find are complicated math unsolved problems which require quite deep math knowledge that is not really taught at my gymnasium.
Are there any open problems which fit me?

I know some easy problems such as: Is there any odd perfect number? Is 10 a friendly number?...
I'm much more interested in algebra, geometry, calculus and trigonometry than numbers alone.
I like finding a way/method using math symbols, I need problems which do not require big-number calculations.

Thanks for help...

Mu naught

what makes you think those two questions are easy?

Atran

By 'easy' I mean that it's easy to understand the question. For instance, I know what a perfect number is, so "is there any odd perfect number" question is understood by me.

Simon Malzard

try this? http://en.wikipedia.org/wiki/List_of...in_mathematics

VeeEight

Most of these unsolved problems have been studied for a while and as a result, mathematicians have developed complicated tools and abstractions to helps them with these problems. The modern student would build a foundation studying things like abstract algebra and analysis - building your knowledge of decades of math while also building your problem solving skills - so that you can study these problems later. This is not to discourage you from finding an odd perfect number, but it may take some time.

I would suggest going through Putnam (math competition) style problems if you are looking for a challenge at problem solving.

Tommo1

Here's a one that's a bit physics and a bit maths but maybe too easy.
1/R=1/R1 +1/R2 for parallel resistors.
How do you produce examples of this with whole number values only?
e.g. R1=14, R2=35 giving R=10.
R1=21, R2=28, R=24 gives exactly R=8.
R1=1400, R2=2600 produces 910 ohms.

Xitami

[latex]\frac{1}{100}+\frac{1}{390}=\frac{1}{82}[/latex]

[latex]\frac{82-79.59}{82}< 20\%[/latex] E12 E series: Capacitors and resistors

Tommo1

You engineers will be the death of mathematical exactitude!
R1=25461230 ohms
R2=25375670 ohms
In parallel R(total)=12709189 ohms (exactly)!

Xitami

Stan Ulam
"pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points"

Tommo1

Hi Atran, this problem doesn't require algebra, geometry, calculus or trigonometry. It is only arithmetic! So get a pencil out and a scrap of paper. Here's another example...
R1=10553063310 ohms
R2=154064581051 ohms
R (total) is still a whole number.

Tommo1

In reply to Xitami, Georg Ohm did okay out of the mathematical approach. It took Bavaria a while to realise it though. Stan Ulam is impressive too though! As is Stanisław Lem, an idea: explosive!!!