DemiSemi
Five shapes a day. One straight line to cut each one into two equal halves. Down to the hundredth.
The idea
Five shapes a day. For each one, you draw a single straight line that cuts it in two. The goal: two pieces with exactly the same area.
Draw the line in one motion: press, drag, release. The cut is the line through your starting point and your end point, extended edge to edge. You get one try per shape, and the cut is final when you let go.
Scoring
Both pieces are shown to the hundredth (A 49.97% and B 50.03%). How far off you are is the distance from 50: here, 0.03.
DEAD ON (off by up to 0.1): 100 points. CLEAN (up to 0.5), NOT BAD (up to 2), and WONKY (up to 5): 100 points minus 20 for every point you’re off. Anything more: MISS, 0 points.
The perfect cut
Whatever angle you pick, there’s always a parallel cut that splits the shape into two exactly equal halves. After each cut, it shows up as a dotted line, along with how far it was from yours, so you can see exactly how close you came.
The shapes
They’re real shapes: countries, islands, lakes, US states, plus one landmark and one object every day, photographed and cut out. Maps are drawn north up, in an equal-area projection, so the area shown when you cut is the area of the outline you see.
Every day
New shapes drop at midnight Eastern Time. Everyone cuts the same shapes, and you can see how you stack up against the day’s players.
Guides
- Why we’re all bad at judging area : Your eyes compare lengths, not areas. Here’s why splitting a shape into two equal halves is so much harder than it looks.
- A perfect 50/50 is always possible. Here’s the proof. : Whatever angle you pick, a perfect cut exists. The intermediate value theorem explains why, and the ham sandwich theorem takes it even further.
- Going through the center isn’t enough : Does a line through the middle of a shape always cut it in half? Sometimes. The humble triangle shows how aiming for the center can land you a MISS.
- 7 tips for cleaner cuts : Cut where the shape is narrow, trade bumps for bulges, never forget the holes: seven simple habits that will get your cuts closer to 50/50.
- Why maps lie about size : On many world maps, Greenland looks as big as Africa. How the Mercator projection warps area, and how DemiSemi draws its countries and states.
- How DemiSemi scores your cut : The shoelace formula for area, the Sutherland–Hodgman algorithm for the cut, a binary search for the perfect line: the whole calculation, in plain English.
From the same maker : RicRac. Seven questions a day. Stop the counter as close to the answer as you dare, without going over.
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