Question

explicit proof for area!

Answer 1

@ikram002p

Answer 2

Are you ready to explain this ^_^

Answer 3

yeah , so whats the rule /formula ur wanna prove ?

Answer 4

Good thanks, let's pick easy one haha. for rectangle since many other are related to it

Answer 5

ohkkk :)
let this be our rectangle

Answer 6

alright!

Answer 7

ok wait i think ill start wih the square lol

Answer 8

okay whatever makes it better ^_^

Answer 9

ok for integer number sides


so terns out area = number of units in arrow * side
or area =number of units in column * side

then area =side^2

Answer 10

So the idea is to count how many unit square for column and row
to form the area is it?

Answer 11

yep that was the first notation , and they know its true for all rational number
but yet couldnt find geometric proof .. so we needed something algebraically to prove it

Answer 12

i see, so there is algebraic proof to this?

Answer 13

there is but it well frust u out with axiomatic system :P
lets consider this one to be valid xD cuz it helps in other proofs
and maybe someother ltr , ill show u how to prove , real proof

agree ?

Answer 14

Okay, that illustration was logical. you can proceed with the proof
let's see if i get frust lol

Answer 15

ok , i might have an idea about history of math for the rational approch
it was the same only there reduced the units into small units


i wanna go through other proofs since we started it as history of math