MathVoyage · First Voyages
Touch mathematics before you study it
Begin with a short question, change something yourself, notice a surprise, and enter the viewpoint of a mathematician.
27's strange journey
If a number is even, halve it. If it is odd, triple it and add one. Predict how far this two-line rule will travel.
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A world without zero
What happens to calculation and place value when “nothing” cannot be written as a number? Erase zero and feel the gap it fills.
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The moment a triangle becomes a rectangle
Cutting and rotating a triangle does not destroy its area. Watch the pieces reassemble into a rectangle and discover the formula with your eyes.
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The hidden fractal in Pascal’s triangle
Pascal’s triangle is built by adding the two entries above each new cell. Color each entry only as odd or even and look for a repeating triangle.
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How numbers dance around a clock
Keep adding the same number on a 12-position clock and discover why some jumps visit everything while others get trapped in a tiny loop.
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The streak illusion in probability
Assume independent flips of a fair coin. Distinguish the rarity of a past streak from the probability of the one flip that comes next.
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A small conjecture and its counterexample
A prime is an integer greater than 1 with no positive divisors other than 1 and itself. Test a formula that seems to make primes and find the one counterexample that overturns the claim.
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