Sorry for digging up old thread.
If you haven’ done Youngs Double Slit experiment in class at some point: The experiment
Do it, it’s really cool (you might need a laser). This shows that light is behaving as a wave.
Both of lights properties can be shown by shooting one and one photon trough a double slit, you will still see this interferencepattern after n photons. (1 photon will light up one spot on the background, thereby also a particle).
Some source for that (sorry for Wikipedia entries, but they should be somewhat correct): Wikilink
You can also read about it here: Wave–particle duality
Over to science. Nothing in science is based on absolute precision.The scientific method is based on measurement and models that resembles them. Therefore they can be proved wrong or inaccurate.
A little source for that: Source
Math. Nothing here can be absolutely “proved”. This is because math is based assumptions. A great example of one of these are Euclid’s axioms and postulates. They cannot be proved, but we assume they are right. The books of Euclid’s defined what most of us call geometry today, and did all of the proofs based on the axioms and postulates.
The axioms and postulates can be found here:friesian.com/space.htm
After some time a bunch of really smart people found out that Euclidian geometry just wasn’t wide enough, and made nonEuclidian geometry. One proof in it is for example that the sum of the angles in a triangle increases as the area of the triangle decreases. This cannot be done using Euclidian geometry where the sum of the angles always is 180 degrees.
Source
What i’m coming to here is that nothing in science is set in stone, and can always change. “Silly things like a square circle or a two sided triangle” can happen. Our logic is based on our perception of the world. We cannot know if something is absolutely true.
sidenotes:

I could argue that you get one two sided triangle just by using the unit circle and use the definition of sinus. Then watch what happens with sin(x) when x approaches 0 the side of the triangle will get smaller and smaller, until sin(0) where you got a “triangle” with two equally long sides(both are 1), and one side that is 0; two corners and still a “triangle”.

The square circle can occur in nonEuclidian space. For example where a unit circle looks like a square en.wikipedia.org/wiki/Lp_space

“i = e/r”. I can also throw around equations that is about electronics, look:
The Laplace equivalent expression of a capacitor is V(s) = 1/(sC)I(s)+V0/s
Source

If some of my formulations of words are somewhat strange, i’m sorry. English is not my first language.