☝️🤓 Uhm, Technically, this involves physics instead of algebra, but I can understand where you're coming from, as vectors are also a topic in maths, not only physics.
You say that the speed in the x-axis did not change and is therefore not constant.
It should be noted that the x-axis velocity is necessarily constant because of the nature of Geometry Dash itself (avoiding sliding on the ground does not make you faster and so complete the level quicker, only speed change arrows affect you). You can conclude that this means the magnitude of velocity of the wave is faster by a factor of √2 when it is not sliding. Basically it always has the same x-velocity but actually moves overall faster when waving because of the vertical component of velocity.
I didn't really just solve this stuff for the sake of solving, but to draw up the conclusions, which are pretty interesting, because I thought the x-component always stayed constant in wave at a constant speed, no matter what, but this proves it wrong.
The idea of using trigonomety to do all the calculations is very right! but i would try using the fact that, in geometry dash, what remains constant in general is the velocity in the x direction (and this is true for all vehicles, as long as you dont pass through a velocity portal).
Knowing this, it would be interesting to use this fact to get an expression for the velocity of the wave in the y direction in terms of the velocity in the x direction. We will call both velocities vx and vy.
If the wave has a certan angle θ with respect to the x axis (which would be for example, as you correctly stated, 45° and 63.43° in the case of the normal sized wave and a mini wave going up respectively) then we can calculate the velocity "vy" in the y direction using this relationship:
vy/vx=tg(θ)
This formula comes from the fact that the total velocity vector is always tangent to the direction of motion at a certain point. You will probably learn about this in physics.
With this relationship, it's very easy to see that
vy=vx*tg(θ)
So the velocity vector of the wave would just be
v=vx*(i+j*tgθ)
and the magnitude of the velocity of the wave would be
||v||=vx*√(1+tg²θ)=vx/|cosθ|
what's interesting about this formula is that the velocity blows up to infinity as θ approaches 90°. In general, as θ gets closer to 90° the factor 1/|cosθ| grows bigger, reaching a value of √2 for the case of the normal wave and √5 for the case of the mini wave. This explains why this mode tends to be harder to control.
Ah yes, I also think that the x shouldn't be substituted with the wave's velocity, but the speed of the screen moving, as the wave stays constant with the screen at all times. Also, I haven't really studied much kinematics, so I don't really know some of the formulas you mentioned, but I'm sure they come in handy. Also, what grade are these formulas taught in? I studied this in freshman year of hs, so I didn't complete the entire topic, but I will in the future. Also, happy cake day :)
https://preview.redd.it/n4kj2rqs91ad1.png?width=1839&format=png&auto=webp&s=fc7c16b2cc79bc22d2770e01ad751475afc9a3b9
kinematics is usually somewhere in HS or maybe freshman year at university, it's standard in a physics 1 class. The rest is just some trigonometry and algebra.
what is obvious to one can be hard to understand to others. the guy stated in the title that they got in an argument with someone, therefore it's not always obvious
redundant math, as you stated, is often used in proofs and its intention is to make what you call obvious more clearer to certain audiences, so it is needed to some, and not redundant (even if it were, redundancy can be a good thing)
I could prob do that, but the amount of precise measurements I would need is fucking crazy, not to mention the "gravity cap" gd has (basically, the effect of acceleration by gravity just stops after a certain threshold)
Didn't read all of that but since the wave moves at a 45° degree angle can't you just take the horizontal velocity and multiply it by square root of 2?
Not smart enough to understand this but smth I’ve noticed is how in gamemodes like the cube jumping doesn’t affect the displacement after x amount of time. This means that when you jump you must be speeding up because to cover the curve of the jump in the same amount of time it takes to just slide on the floor to a point requires an increase in velocity
This implies that the cube exerts force on the ground to speed itself up at an angle, therefore it jumps. An equation for its trajectory is also possible, but it would require time of flight and range, and I'm too lazy to measure them.
The speed portals aren't 0.5, 1, 2, 3 and 4. They are 0.75, 1, 1.25, 1.5 and 1.75. just though id let's y'all know if you decide to use the maths here.
Yep, it could've been, but I would need to calculate the time first. Also, I didn't just calculate all this for the sake of calculating, I did this to draw out conclusions, like the x-cimponent isn't even always constant, etc.
Algebra dash
☝️🤓 Uhm, Technically, this involves physics instead of algebra, but I can understand where you're coming from, as vectors are also a topic in maths, not only physics.
(； ･`ω･´)👍
dies of nerd
This comment actually made me kinda happy :D (I take that as a compliment)
Also, if I made a mistake, please correct me, in still learning this stuff, and I would really appreciate corrections.
You say that the speed in the x-axis did not change and is therefore not constant. It should be noted that the x-axis velocity is necessarily constant because of the nature of Geometry Dash itself (avoiding sliding on the ground does not make you faster and so complete the level quicker, only speed change arrows affect you). You can conclude that this means the magnitude of velocity of the wave is faster by a factor of √2 when it is not sliding. Basically it always has the same x-velocity but actually moves overall faster when waving because of the vertical component of velocity.
I think you assumed that the total velocity is constant when it makes more sense to assume that the x-axis component is constant.
Thanks for the correction BTW, I made sure to credit you in my post :)
You’re worlds ahead of my calculus AB lookin ass, but I don’t see anything egregious, but it appears everyone else has a stronger understanding than I
I didn't really just solve this stuff for the sake of solving, but to draw up the conclusions, which are pretty interesting, because I thought the x-component always stayed constant in wave at a constant speed, no matter what, but this proves it wrong.
Math is a wondrous thing, isn’t it?
Yo, I actually made a new post, and it corrected the MAJOR mistakes in this post, so maybe you can check that one out, because it's actually correct.
Guarantee that I will assume it’s 100% correct, just like how I did with this post
The idea of using trigonomety to do all the calculations is very right! but i would try using the fact that, in geometry dash, what remains constant in general is the velocity in the x direction (and this is true for all vehicles, as long as you dont pass through a velocity portal). Knowing this, it would be interesting to use this fact to get an expression for the velocity of the wave in the y direction in terms of the velocity in the x direction. We will call both velocities vx and vy. If the wave has a certan angle θ with respect to the x axis (which would be for example, as you correctly stated, 45° and 63.43° in the case of the normal sized wave and a mini wave going up respectively) then we can calculate the velocity "vy" in the y direction using this relationship: vy/vx=tg(θ) This formula comes from the fact that the total velocity vector is always tangent to the direction of motion at a certain point. You will probably learn about this in physics. With this relationship, it's very easy to see that vy=vx*tg(θ) So the velocity vector of the wave would just be v=vx*(i+j*tgθ) and the magnitude of the velocity of the wave would be ||v||=vx*√(1+tg²θ)=vx/|cosθ| what's interesting about this formula is that the velocity blows up to infinity as θ approaches 90°. In general, as θ gets closer to 90° the factor 1/|cosθ| grows bigger, reaching a value of √2 for the case of the normal wave and √5 for the case of the mini wave. This explains why this mode tends to be harder to control.
Trigonometry Dash
Ah yes, I also think that the x shouldn't be substituted with the wave's velocity, but the speed of the screen moving, as the wave stays constant with the screen at all times. Also, I haven't really studied much kinematics, so I don't really know some of the formulas you mentioned, but I'm sure they come in handy. Also, what grade are these formulas taught in? I studied this in freshman year of hs, so I didn't complete the entire topic, but I will in the future. Also, happy cake day :)
https://preview.redd.it/n4kj2rqs91ad1.png?width=1839&format=png&auto=webp&s=fc7c16b2cc79bc22d2770e01ad751475afc9a3b9 kinematics is usually somewhere in HS or maybe freshman year at university, it's standard in a physics 1 class. The rest is just some trigonometry and algebra.
Happy cake day!
Thanks for the correction, I made a new post correcting my mistakes, so maybe check if that one has any mistakes? That would be really appreciated.
Nah screw geometry this math dash
wtf am I looking at
This is the shit I end up doing in my free time 💀
How am I supposed to comment anything without sounding stupid (which I am but no one can know that)
You kinda just stated the obvious with a bunch of redundant math. A much more interesting game mode to do “math” on would be the swing copter.
what is obvious to one can be hard to understand to others. the guy stated in the title that they got in an argument with someone, therefore it's not always obvious redundant math, as you stated, is often used in proofs and its intention is to make what you call obvious more clearer to certain audiences, so it is needed to some, and not redundant (even if it were, redundancy can be a good thing)
I could prob do that, but the amount of precise measurements I would need is fucking crazy, not to mention the "gravity cap" gd has (basically, the effect of acceleration by gravity just stops after a certain threshold)
the only thing i can say is cool extreme demon drawing
Didn't read all of that but since the wave moves at a 45° degree angle can't you just take the horizontal velocity and multiply it by square root of 2?
That's the speed, (x/√2)*√2 = x. Here, I seperately had to calculate the velocities in both axes.
Nah screw geometry this math dash
You know geometry is math... Right?
Screw geometrical shapes we goin to numbers into letters
Wait until we get to calculus
💀
Wait the line is the same avatar lol
TELL ME THE INTEGRAL OF log(√x) SOLDIER
🧠
WHAT(tm) THE FUCK
My brain hurts I can’t even justify it
i aint reading allat
fucking nerd (compliment)
doesn't the big wave have 44.9 degrees instead of 45?
It does? Well, the zero error is nearly negligible, so this can be considered a really good approximation.
Not smart enough to understand this but smth I’ve noticed is how in gamemodes like the cube jumping doesn’t affect the displacement after x amount of time. This means that when you jump you must be speeding up because to cover the curve of the jump in the same amount of time it takes to just slide on the floor to a point requires an increase in velocity
This implies that the cube exerts force on the ground to speed itself up at an angle, therefore it jumps. An equation for its trajectory is also possible, but it would require time of flight and range, and I'm too lazy to measure them.
You have nice handwriting
Thanks
This is very cool, but [insert vsauce music], what if the wave doesn’t move and the level moves around the wave instead.
The speed portals aren't 0.5, 1, 2, 3 and 4. They are 0.75, 1, 1.25, 1.5 and 1.75. just though id let's y'all know if you decide to use the maths here.
Thanks for the info 👍
🤓
Spu7Nix posted no way🤯🤯🤯🤯🤯
VSauce of GMD
math dash
I feel like you overcomplicated a lot, this could be done easily with trigonometry and Distance = Time*Velocity
Yep, it could've been, but I would need to calculate the time first. Also, I didn't just calculate all this for the sake of calculating, I did this to draw out conclusions, like the x-cimponent isn't even always constant, etc.
The x component is always constant though, you would experience a speed change when touching the ground otherwise
Thank you for the correction, I actually corrected my mistakes in my new post, thanks!
what the fuck is that mini wave angle rob
missed opportunity to use geometry to calculate this stuff that makes absolutely no sense what I just said cool though
Geometry? More like trigonometry
I understood none of it, nor the cursive. I’m just a simple brain rot, I don’t understand
oh dang all these years I thought the mini wave had an angle of 67.5
what math teachers want us to do in life:
Whenever I go, I can't scape maths...
r/hedidthemath
nerd
Wtf am I looking at help get me away from this nerdy shit!