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Nov
2
awarded  Nice Answer
Nov
2
revised Tiling of squares in instances of Pythagoras Theorem
small edit
Oct
31
revised Tiling of squares in instances of Pythagoras Theorem
addition
Oct
31
asked Tiling of squares in instances of Pythagoras Theorem
Oct
27
comment What is the simplest proof of the pythagorean theorem you know?
Also, how do you know that with squares of those sizes you end up with a right angle between A and B (without already knowing the pythagorean theorem)?
Oct
22
awarded  Notable Question
Oct
17
awarded  Favorite Question
Sep
17
revised Intuition behind Matrix Multiplication
small cleanup
Sep
16
awarded  Yearling
Sep
9
awarded  Nice Answer
Jul
12
comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
@Timbuc How is it inductive? Because addition, multiplication by irrationals and exponentials are inductive?
Jul
12
comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
I don't understand the talk about 'implicit induction'. The proof method asked for should not use an induction hypothesis, and they don't. Any implicit induction is like saying "Gaussian elimination inverts an $n\times n$ matrix" or "$2^n$ is total" are proved implicitly by induction because they involves natural numbers.
Jul
12
comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
@Timbuc It is not necessary that $F_n$ be defined inductively; it could be defined using Binet's formula from the beginning and then later proved that the equation for $F$ in terms of smaller values holds. No necessary induction.
Jul
3
awarded  Good Question
Jun
13
comment Why is it that this gives a good approximation of $\pi$?
What is a reason and what is a coincidence? This is realted to the mathematical phenomenon of almost integers, calculations involving seemingly random irrationals that turn out to be almost an integer (your choice could be rearranged to say $\frac{\ln^2 11}{\ln 100 \pi} \sim 1$). A reasonable 'why' answer might come from equations that involve floors (like powers of the Fibonacci constant).
Jun
12
comment What are “instantaneous” rates of change, really?
To reword what others have said, 'instantaneous' is just a metaphor to help with intuition. In the metaphor, there's a contradiction, movement over no time at all which really isn't movement. So that's a problem with the intuition, not the formal mathematics.
Jun
10
awarded  Notable Question
Jun
9
revised What is the smallest unknown natural number?
added lower bound picture
Jun
2
comment Why doesn't a Taylor series converge always?
Can you give some of these well-known examples?
May
26
comment General solution to a system of non linear equations with a specific pattern
Have you tried solving less complex systems, for example all these systems without the first equation ($a^2 + b^2 + ...$), or just the first two equations? or where $x^i$ all equal 0? Those kinds of simplifications may (or may not) be easier to solve and may give hints on how to solve the bigger problems.