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Cake day: June 14th, 2023

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  • TheOakTree@beehaw.orgtoScience Memes@mander.xyzturkey pot pies
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    8 months ago

    (1/2)×θ×r^2

    is the area of a circle sector, like a slice of pie.

    (1/2)×sin(θ)×side1×side2

    is the side-angle-side formula for the area of a triangle.

    We know that the triangle encompassed by the sector has two sides that are equal to the radius, so we replace side1×side2 with r^2. Since the area of the arc segment is equal to the area of a sector minus the triangle, we can subtract triangle area from sector area to get

    (1/2)×(θ-sin(θ))×r^2

    which is the area of the arc segment, as shown with pie in the picture.





  • A ton, actually. I’m not very engaged in it, but every time some friends convince me to play something on Fortnite with them, I can’t help but notice the section of hundreds and thousands of gamemodes with custom rules, items, mechanics, and so on.

    For example, I see many clones of bed wars from Minecraft, third-person CoD clones, RP servers, base/colony building gamemodes, zombie survival modes, etc. It effectively has a sandbox game maker inside of the regular Fortnite, alongside Rocket Racing (racing game) and Fortnite Festival (rhythm game). It’s a very fleshed out environment, although it doesn’t have the same potential for custom assets that Roblox does.