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Why must five points contain a convex four-sided shape?

Four dots can fail to make a convex four-sided shape if one sits inside the triangle formed by the others. Add a fifth dot, with no three on one straight line, and some four must form a convex quadrilateral.

5–7 min

Questions you could explore

  • Draw five points with no three on a straight line: how can you find four forming a convex quadrilateral?
  • Why does the guarantee say some four points rather than every choice of four?

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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

Maths and statistics5–7 minAn 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?

Maths and statistics

How is random sampling different from random assignment?

A study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

3–5 min

How is random sampling different from random assignment?

Maths and statistics3–5 minA study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

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 five points contain a convex four-sided shape? | Speech Topic | speaking.app