Gregory's ServerPosted without further comment 🔻
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79 comments
  @bigfoot nice try, but a square has four *internal* right angles, with parallel opposite sides, among other properties 😉      @salgood Those angles are only 90 degrees at an infintesimally small point where the line meets the curve so you could argue they dont exist @RavenLuni @salgood Well, that's the definition of an angle, right? An infinitesimal distance away, there is no angle anymore. @erwinrossen @salgood I always saw it as the intersection of 2 vcetors but I guess youre right @RavenLuni @erwinrossen @salgood i think this is drawn using a polar coordinate space rather than a Cartesian space. In a polar sense, the lines are all either moving longitudinally or laterally, so the 90 degree rule checks out.  @RavenLuni @erwinrossen @salgood a square is also defined as the opposing lines have to be parallel. (As they are a subbody of a parallelogram) @NafiTheBear @RavenLuni @erwinrossen @salgood Common definitions also include that the diagonals intersect at a set of right angles too. @erwinrossen @RavenLuni @salgood More formally, the angle between two smooth curves at a point is defined to be the angle between the tangent lines at that point. A bigger problem with the image is that when you talk about some figure made up of arcs, you should always measure your angles on the same side (inside or outside): really the shape shown has two 90 degree angles and two 270 degree angles. There are four parameters : the small partial circle radius, the arc radius, the arc angle and the "side" length. @lauxmyth out of curiosity how do you interpret the center of an object. I get that you are having a lark and talking about the lines that form the perimeter but really like curious   You mean if the plan was non-Euclidian? Of course, it could work, probably! It would kind of breaks the joke though. "On a plane of a shape you can't even imagine, this is a square!" 😅 Yes, but that's not the point. Most people don't know about non-Euclidian geometry, I guess it would be beyond them to imagine a plane the shape of a trombone...   I'm saving this for the quadrilaterals unit. Although, I do think we define "sides" to be "straight lines" which has its own problems as an undefined term. Still I like this.   But how do you define which side is the "inside" and which one is the "outside" ? How do we make that concept well defined?    It's been way too long since school, but wasn't the definition also about the angles being inside the shape?  @salgood@socel.net guy who just discovered non-euclidian geometries for the first time       @salgood Vaguely remember having to work out the angle that the two straight lines intersect at in a maths lesson. Think it’s 42 degrees.   @salgood @mistercharlie Good to see folks finally getting red pilled on the liberal geometry scam @salgood technically it should be a parallelogram not just a generic shape, but using radial space the definition still holds so hats off to you! 💜💜💜       |
@salgood cursed