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Why must one point on a map lie above its real location?

Lay a smaller continuous map of a disk-shaped region entirely inside that region. At least one point on the map must sit directly above the place it represents, even if the map is shifted or rotated. Explore the fixed-point theorem behind the puzzle and why its geometric assumptions matter.

5–7 min

Questions you could explore

  • What does a fixed point mean for a smaller, continuous map laid entirely inside a disk-shaped region it represents?
  • How do tearing the map or moving it outside that region change the assumptions behind the guarantee?

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Maths and statistics

When one long wait changes the average

An average wait can sound straightforward until one person waits much longer than everyone else. The mean and median offer two ways to summarize that same group. Their different responses to an unusually large value raise a practical question: what do we want an average to tell us?

5–7 min

When one long wait changes the average

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3–5 min

How is random sampling different from random assignment?

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Maths and statistics

The leap years the Gregorian calendar skips

Most people learn that a leap year happens every four years, yet the year 1900 had no February 29 while the year 2000 did. Because Earth's orbit takes slightly less than 365.25 days, the Gregorian calendar skips three leap years every four centuries to keep the calendar aligned with the seasons.

2–3 min

The leap years the Gregorian calendar skips

Maths and statistics2–3 minMost people learn that a leap year happens every four years, yet the year 1900 had no February 29 while the year 2000 did. Because Earth's orbit takes slightly less than 365.25 days, the Gregorian calendar skips three leap years every four centuries to keep the calendar aligned with the seasons.

Why must one point on a map lie above its real location? | Speech Topic | speaking.app