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@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.Which one?
The heck is the deleted real neighborhood?
all
teeno hi nahi hue
i have no idea 💀
First one, equilateral
why?
You will always end up with a root three sneaking into the coordinates with an equilateral triangle
how
heh
It's because we use rectilinear coordinates
wut
Lattice points are the vertices of squares
oh that's smart
Options c b a
Last one the parameter is r
wtf does 3 even mean
The slope is fixed for a straight line.
bro what is you yapping about 💀
If your parameter were θ, you'd have a circle
think about it with pythagoras logic
if the side length of the equilateral is 'a'
WHATS LATTICE POINT WHERES LATTICE POINT WRITTEN
then the height will be, by pythagorean theorem, sqrt(a^2 - a^2/4)
Lattice points matlab integer coordinates
= root 3 a / 2
now tell me
height root 3 a / 2 hai
how will you ever end up with every coordinate rational
what does coordinate being rational have to do with the distance it has with some other point?
ok it makes sense to me but i haven't a clue how to explain it
so i might be wrong
any example of this happenieng?
consider the base parallel to the x axis with some rational x coordinate
You see, when all your coordinates are based on your axes being perpendicular to each other, you end up having irrational coordinates for a shape with no interior angle that is = 90°
one of the vertices will have that rational x coordinate + height (root3a/2)
when you end up with irrational
It's about the orthonormal system but I'm getting ahead of myself here
please explain in simple terms
An affine basis would change things.
doesnt the normal form of a line where you obtain the Perpendicular dist of a point on a line from the Origin have theta as a parameter
But that's not what you have. It's the parametric form.
you're being very presumptuous about what people know and don't know
simple terms
I avoid this section for that reason lol
I'll stay out of this
Sorry
oh so ths is just
an intrinsic property?
just happens?
Mhm
Yup
doubleroot
DoubleRoot
Equation of a Straight Line - Parametric Form | Doubleroot.in
Derivation of the parametric form of the equation of a straight line in the Cartesian plane.
Because you're measuring with perpendicular axes
is there a rigorous proof that can be understood by us
Let me see.
woahh
i see isee
But complicated, but I found this .
TLDR; if you take a lattice point, and draw a line with inclination 60°, it won't intersect another lattice point, because the slope is irrational
ohh
i see
so its just a law of coordinate geometry then ki it will just never happen for rational
got it
Yup
Though I suppose it is quite different in 3 dimensions
what about 3
that's pretty cool
I haven't checked really
It is.
idk idc about 3D im cooked in 2D im boutta get smeshed in 3D
Works a lot better with linear transformations ngl but that's not the focus here.
god knows what deleted real neighbourhood means
Had a test on 3d today
This
cooked?
well ill ask sir about 3
4?
3d is fun
first is equilateral
No Planes for mains, so I got 90/100. Should get 95
yea got that
yeah planes was the only hard part
Ok, wrong place to talk
noice
4?
oh ha
r
wtf is deleted
got it
neighbour shit
parametric
who knows
yea got it
thank yall
+solved @Opt @Nimboi
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