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Cake day: July 10th, 2023

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  • ltxrtquq@lemmy.mltoScience Memes@mander.xyzSquare!
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    1 month ago

    Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ

    You’re using the derivative of a polar equation as the basis for what a tangent line is. But as the textbook explains, that doesn’t give you a tangent line or describe the slope at that point. I never bothered defining what “tangent” means, but since this seems so important to you why don’t you try coming up with a reasonable definition?


  • ltxrtquq@lemmy.mltoScience Memes@mander.xyzSquare!
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    1 month ago

    I think we fundamentally don’t agree on what “tangent” means. You can use

    x=f(θ)cosθ, y=f(θ)sinθ to compute dydx

    as taken from the textbook, giving you a tangent line in the terms used in polar coordinates. I think your line of reasoning would lead to r=1 in polar coordinates being a line, even though it’s a circle with radius 1.


  • ltxrtquq@lemmy.mltoScience Memes@mander.xyzSquare!
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    1 month ago

    Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ

    I think this part from the textbook describes what you’re talking about

    Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.

    And this would give you the actual tangent line, or at least the slope of that line.


  • ltxrtquq@lemmy.mltoScience Memes@mander.xyzSquare!
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    1 month ago

    Polar Functions and dydx

    We are interested in the lines tangent a given graph, regardless of whether that graph is produced by rectangular, parametric, or polar equations. In each of these contexts, the slope of the tangent line is dydx. Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ. Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.

    From the link above. I really don’t understand why you seem to think a tangent line in polar coordinates would be a circle.


  • ltxrtquq@lemmy.mltoScience Memes@mander.xyzSquare!
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    1 month ago

    A straight line in polar coordinates with the same tangent would be a circle.

    I’m not sure that’s true. In non-euclidean geometry it might be, but aren’t polar coordinates just an alternative way of expressing cartesian?

    Looking at a libre textbook, it seems to be showing that a tangent line in polar coordinates is still a straight line, not a circle.



  • 1. OWNERSHIP

    By accepting these terms, you acknowledge and agree that you do not own or have any proprietary rights in the Game or any Mods you create, except as specifically mentioned here. Any Mods you create are your property only if they consist only of your original creative work. To the extent that any element of your Mod includes or is derived from the Game’s intellectual property (such as code, themes, characters, names, stories, dialogue, locations, artwork, sounds, music, and visual effects), you agree that all intellectual property rights therein, whether they are registered or not, are owned by Larian Studios and its licensors.

    I’m not sure I believe you about your first point.




  • The Black Pool is a game I decided to try recently. It reminds me a lot of Returnal in terms of visuals and gameplay, but I don’t expect the story to evolve much beyond the initial “kids lost in the woods trying to get home.”

    It’s a 4-player roguelike where you get to choose random elements to slot into different abilities, namely a Primary, Secondary, and AOE attack as well as a jump, dodge, and once-per-world ‘rally’ buff. Each element makes the ability act differently, like a light primary is a slow charging piercing laser while wind is a projectile with knockback, and you also get to upgrade your elemental abilities after each stage you clear. I’m only about an hour into it so far, but I definitely think it deserves a little more than the 29 player peak it got right after it launched.








  • Found it

    Starting Season 10, all new heroes will be immediately unlocked when they launch. All existing heroes will also be unlocked for players. This means that heroes will no longer need to be unlocked through the Battle Pass to be playable in all game modes.

    New players will still need to complete the first-time user experience to unlock heroes as they learn the ropes. Once the heroes from the original Overwatch roster have been unlocked, all Overwatch 2 heroes will also become available.

    So unless there was another change, new players still need to play/win games in order to unlock the full roster.