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As part of my secondary geometry class I like to hook students by presenting real-world examples (usually images I find online or have taken myself) of different geometric shapes from real life. For instance, a lesson on the area of a circle might start out with a picture of a pizza pie or a lesson on the midsegments of triangles might start out with a picture of the Triforce. However, there are some geometric figures that I have had a hard time finding interesting, real-world examples of. Those figures (and I know I am forgetting a bunch..) are:

  • Segment of a circle
  • Secant line
  • Trapezoid (Isosceles or not)
  • Inscribed angle
  • Parallel lines cut by a transversal

I was wondering if anyone had any ideas for these geometric figures of interesting, real world examples? Also, I think it would be great that if people are aware of really cool real world examples for the more "standard" geometric figures to post those as answers as well. For instance, the Dockland Building at the Port of Hamburg is an astoundingly perfect parallelogram :) enter image description here Having a collection would be very helpful for teachers because I have not found a better way to get my students right into the groove by starting class off with a brief discussion about an interesting picture!

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    $\begingroup$ For some of these, start by closing your eyes and imagining where in life you have seen such shapes. I can imagine leaning books on a bookshelf and train tracks intercepting a road at an angle for your trapezoid and for parallel lines intercepted by a nonperpendicular line. Doubtless a search of an image database will come up with other examples present in the world. Gerhard "You Can Ask Your Students" Paseman, 2015.03.05 $\endgroup$ – Gerhard Paseman Mar 5 '15 at 17:33
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    $\begingroup$ There is an MO question on mathematical sculptures. Mostly they seem to ornate for the present purpose, but some might be relevant. $\endgroup$ – quid Mar 6 '15 at 12:09
  • $\begingroup$ Quadrilaters: there's also kites (normal kite). And concave kites (also actual kites). Also the Star Trek insignia. And arrowheads. $\endgroup$ – guest Jun 20 '18 at 21:57

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A nice challenge for a calculus class with a little physics: If particles are thrown out from a common point in all directions at the same speed, then allowed to fall freely, the shape they will sweep out is a parabola. (Of course, the trajectory of each particle is also a parabola, that's a simpler fact.) The Fourth of July might suggest some examples:

enter image description here

enter image description here

When I was in high school, I saw a cutting board lying on an angle in a sink with the water pouring from the faucet onto a point on it. The water splashed out to form a parabolic arc. I wonder if you could actually bring something like that into the classroom and trace the edge of the water?

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From an MathOverflow question, Six yolks in a bowl: Why not optimal circle packing?:


         
          Six yolks in a bowl.

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Many molecules have striking shapes. For example cubane: https://en.wikipedia.org/wiki/Cubane

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    $\begingroup$ Short and link-only answers are discouraged. A summary of the contents of the link would improve the answer. $\endgroup$ – Tommi Brander Jan 22 at 12:17

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