Reverse Engineering
Reverse Engineering
ghost | 7748 Reads | Today I was sitting in science class doing a project on crystal systems (yawn!).
For the project we had to reconstruct the crystal system shapes (Cube, Tetrahedron, ect..) and then count how many faces, edges, and vertices.
When we were done with one, we had to prove we counted correctly, using 1 of 2 formulas provided: FACES + VERTICES = EDGES + 2 FACES + VERTICES - EDGES = 2
so i got tired of counting and decided to try and find an "exploit" to his method. i tried looking for patterns in the answers, nothing..
i started looking everywhere for something and then i noticed, the flaw was the formula!
I started doing some equations using the cube.
Cube: Faces - 6 Vertices - 8
So reversing the formula into giving me the answer to edges..
6 + 8 - E = 2 -6 -6
8 - E = -4 -8 -8
- E = -12
-1 x -E = E -1 x -12 = 12
E = 12
Proof checking: 6 + 8 = 14 14 - 12 = 2
IT WORKED!!
I got excited, finished off doing the rest of them before any one in the class (seeing as one of them had 30 edges.. and it only took me 3 seconds to count and everyone else almost 3 minutes.) and then brought up my paper (and the work to get the reverse engineered formula) to my teacher. He asked me how i finished so quickly and i showed him the formula and everything i did.
This is just a simple little example of reverse engineering, a.k.a. taking information you already know and using it to your advantage, or making it do something it isnt supposed to be doing.
ghost 19 years ago
:| cool I suppose, but you seem to show a total lack of understanding of algebra, it may help to try and convince yourself, FACES + VERTICES - 2 = EDGES means that for a cube 6 + 8 - 2 is a good as answer as 12. But nice anyhow, how are you by chance? Hope I didn't just blast a kiddie…:(
ghost 19 years ago
lol.. nah no "kiddie blasting" was done.. only some information was given.
lol and as for total lack of algebra.. maybe so seeing as im only in the beginning of 8th grade and taking pre-algebra:p
nice try at the kiddie blasting tho man.. only thing u did tho was find a second way to do the same thing, just faster. thx for the tip tho :)
ghost 19 years ago
Lol,, not how I mean, I meant as in you didn't look like you understood algebra. But i realise it because you're just starting the 8th grade, thats why i asked the age. Sorry, I was just trying to explain… Ah forget it you'll realise what I mean later in your course! no attempt at kiddie blasting.:)
richohealey 18 years ago
ok, not trying to flame you and your observation translates nicely to the real world and methods of problem approach, but christ dude, they must take it real slow in the US. by year 8 in aus we've had those algebraic principles bored into us. in fairness i'm in my final year of high school (year 12) and taking the hardest maths in my states syllabus, but geez.
sorry that all sounded a bit harsh. well done
ghost 17 years ago
not everyone in the US takes it slow. i was in the accelerated track so i was taking alg. 1 in 8th grade. my bro was in honors so he was taking alg 2. in 8th grade. :):):o
ghost 17 years ago
Comment about the real nature of algebra in Greece by 17 you should know pretty much about derivative, limits and integral, and stuff like that. i m not sure if i m using the correct terms; if you know about algebra, or maths to be precise i want to give an example: derivative in x0: f'(x0) = ( f(x)-f(x0) )/ x - x0 (integral is the opposite) i think that mathematics can be very exciting, and there are many, difficult problems waiting to be solved
ghost 17 years ago
Nice one, however I believe that the formula was discovered by Euler long long ago, in a galaxy not unlike our own.
ghost 13 years ago
Once in chemistry, we had to balance 50 equations. While all my friends were busy trying to do all of them, I "reverse engineered" it by finding my teacher's answer key. I then proceeded to had in a perfect worksheet in a ridiculous time, completely shocking my teacher. Very useful :D
Lemmink 11 years ago
This is a long long time ago, maybe you're in university now or just hacking banks for your green, but I really want to say this. TO BE FAIR, you really just skipped the first half of the assignment. That's why you finished so fast, A LONG TIME AGO. :right:
neolithicLoser 10 years ago
This is one of the famous Euler result. Its for planar graph. There is an extension of this result which includes platonic solids and other solids with genus > 1. I do not exactly recall the extension formula. It has application in geometric topolgy.