Visual demonstration that all angles of a shape combine to make 360 degrees

  1. As former geometry teacher, I feel like I need to note that this is only true for convex polygons. Concave and self-intersecting polygons are built different.

  2. Since the exterior angles add up to 360 and there are n number of angles where each interior + exterior angle adds up to 180, subtract 360 from n*180 to get the sum of the interior angles.

  3. The angles inside the triangle add up to 180 degrees. There is a nice geometric proof of this (draw a line parallel to the triangle base, going through the triangle tip, then identify angles which are equal to each other. Sorry if this isn't clear, if I had a diagram it would be.)

  4. that's just cool... It's funny, I was always more of an English/History kind of nerd, but I really loved geometry, it was just a fun "you can see it" form of math that I really enjoyed.

  5. Walk in a line and then turn and turn again until you get back to the same spot, by definition you have rotated 360 degrees

  6. i like watching Eddie Woo on youtube. he explains things like why dividing by zero doesn't work, and why the pythagorean theorem is a thing, and lots of similar stuff

  7. In my 29 years of life I've had the WORST time trying to figure it this. You just did want every teacher Ive ever had tried to do, make me understand this.

  8. nice visualization, i always understood this as a car going along the perimeter always takes a 360 turn, works even for concave shapes

  9. Angles can’t really be measured across all the dimensions at a point in a 3D space, as they would normally measure between two lines on a 2D plane.

  10. I knew it as a rule, but to see it play out in picture is something I've never thought of ... think of all the people that will be helped with this visualization!

  11. Well yeah, of course, there is only 360 degrees of motion any straight line can travel in our dimension. It all starts from 1 point.

  12. I wish we had representations like this when I was in school. I thought I was bad at math my whole life, but then I realized it was more the fact that I’m more of a linguistic and conceptual person.

  13. Makes me wish the obvious relationship between mathematics and art was made more prominent in school, it would likely help inspire many kids about the fascinating nature of mathematics 🤓🤌

  14. I learned this in high school geometry, but wish I'd had a visual like this to make me believe it. I thought algebra and geometry were 100% alternative facts (before that phrase existed), so I treated both classes like I was learning a foreign language and that lowered my stress level.

  15. All polygons at least, right? Lines are shapes and some shapes have curved lines where this isn’t true. And that’s only 2D shapes. Sorry I’m very literal.

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