Felt-Tip Geometry

I am pleased as punch (which is, as I understand it, a very pleased drink?) to offer you four new puzzles from geometric visionary Catriona Shearer.

They are arranged in roughly ascending order of challenge, but can be consumed in any order (unlike most four-course meals).

 

Three Little Squares Went Out to Play

catriona 1
The three small squares each have an area of 4. What is the total shaded area?

People kept asking Catriona if this one was a “trick question.” It’s not; just a tasty little hors d’oeuvre, which you may wish to nibble at for a while, or to eat in a single bite. (See the original here.)

 

The Parallelogram of Eternal Balance

catriona 2
What fraction is shaded?

I love this construction. Nothing but midpoints, connected with the elegance and economy of a calligrapher. “I’m sure this is a classic that’s been done many times,” says Catriona, “but it was new to me.”

(See the original here, including a beautiful animated solution, as well as a lovely solution by dissection.)

 

Sunny Dome

catriona 3
The two red arcs are the same length. What fraction of the semicircle is shaded?

Catriona describes this as a riff on her very first puzzle (which I dubbed Garden of Clocks). I’ll take this moment to make the vapid point that, in addition to impeccable geometric taste, Catriona always chooses the perfect colors. (See the original here.)

 

Three Squares and a Slash

Catriona 4
The areas of the squares are given. How long is the line?

Some of Catriona’s puzzles yield to a single geometric insight. This one offers a different kind of pleasure. Catriona explains: “I doubt many people could do this one in their head – I couldn’t – but it makes the highlight reel on account of an unreasonably nice answer.” (See the original here.)

5 thoughts on “Felt-Tip Geometry

  1. What’s the best way to see all of Catriona’s puzzles? I see that you have posted collections 4 (?) times. Is that the complete set so far? Do I need to wade into twitter to find one-off puzzles?

    1. In partial answer to my own question, I think there are at least 5 sets of CS puzzles. Four are tagged “Catriona Shearer, Puzzle Wizard” but this one is not: https://mathwithbaddrawings.com/2018/10/03/twenty-questions-of-maddening-delicious-geometry/
      By title, the list is:
      Twenty Questions of Maddening Delicious Geometry
      Tilted Twins (and other delights)
      Geometry Puzzles for a Winter’s Day
      Six New Geometry Puzzles
      Felt Tip Geometry (this page)

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