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.

 

[Simon43254]

try this? http://en.wikipedia.org/wiki/List_of_unsolved_problems_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]

$\frac{1}{100}+\frac{1}{390}=\frac{1}{82}$

$\frac{82-79.59}{82}< 20\%$ E12 http://en.wikipedia.org/wiki/Preferred_number#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 realize it though. Stan Ulam is impressive too though! As is Stanisław Lem, an idea: explosive!