Percentages can be tricky, because a fifty percent rise followed by a fifty percent fall leaves you below the start.

The longer version

Start with a hundred, add fifty percent, and you hold a hundred fifty. The fall is then taken from that larger amount, so losing fifty percent removes seventy-five and leaves seventy-five. Written as multipliers the result is one point five times one half, which equals three quarters, not one.

The pattern generalises: a rise of x followed by a fall of x always lands you at one minus x squared of where you began, so the loss grows with the size of the swing. Percentage points exist as a separate unit precisely to avoid this trap when discussing rates. Comparing two percentages also requires knowing what base each was taken from.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.