🔮 The Secret Revealed!
Neither Shape Is Actually a Triangle!
The "hypotenuse" is slightly bent. The two triangular pieces have
different slopes, so they don't form a straight line!
Red Triangle Slope
3/8 = 0.375
Blue Triangle Slope
2/5 = 0.400
In Arrangement A, the "hypotenuse" bows slightly
inward (concave), making the total area slightly less than a true 13×5 triangle.
In Arrangement B, the "hypotenuse" bows slightly
outward (convex), making the total area slightly more than a true 13×5 triangle.
The difference between these two fake triangles is exactly 1 square unit —
the "missing" square!
🌀 The Fibonacci Connection
The dimensions 2, 3, 5, 8, and 13 are all Fibonacci numbers!
This isn't a coincidence.
235813
Cassini's Identity states that for any Fibonacci number F(n):
F(n)² = F(n-1) × F(n+1) ± 1
For F(6) = 8: 8² = 64, and 5 × 13 = 65. The difference is exactly 1!
This is why the puzzle works so perfectly — the "error" is always exactly 1 square unit.
The total area of all four pieces is exactly 32 square units in BOTH arrangements.
No area appears or disappears — it's all in the bend of the "hypotenuse"!
📜 History
This puzzle was invented by Paul Curry, a New York City
amateur magician, in 1953. It was popularized by
Martin Gardner in his 1956 book
Mathematics, Magic and Mystery.
The underlying principle of dissection paradoxes has been known since the
16th century. Similar puzzles include
Sam Loyd's famous "64 = 65" chessboard paradox.