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Zero as a placeholder and as a number

Zero can preserve an empty position in a written number. Historical examples distinguish that placeholder role from developing rules for using zero as a number in operations such as addition and multiplication.

3–7 min

Questions you could explore

  • Why would a placeholder alone leave questions about arithmetic unanswered?
  • How do the zeros in a place-value system differ from treating zero as a quantity in a calculation?

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History

Calibrating the radiocarbon clock

Carbon-14 decays at a steady, predictable rate, which makes it look like a simple stopwatch for dating ancient wood, bone, or charcoal. However, the amount of radiocarbon in Earth's atmosphere has varied over the millennia, so an accurate date relies on calibrating the measurement against tree rings and other materials whose calendar age is already known.

4–5 min

Calibrating the radiocarbon clock

History4–5 minCarbon-14 decays at a steady, predictable rate, which makes it look like a simple stopwatch for dating ancient wood, bone, or charcoal. However, the amount of radiocarbon in Earth's atmosphere has varied over the millennia, so an accurate date relies on calibrating the measurement against tree rings and other materials whose calendar age is already known.

History

How do archaeologists work out what happened first?

A deep object is not necessarily the oldest thing at an archaeological site. A later pit can cut through earlier ground, leaving a sequence that has to be reconstructed from relationships between layers.

4–6 min

How do archaeologists work out what happened first?

History4–6 minA deep object is not necessarily the oldest thing at an archaeological site. A later pit can cut through earlier ground, leaving a sequence that has to be reconstructed from relationships between layers.

History

When Britain’s railways needed a shared clock

A timetable becomes awkward when the clocks at its two ends disagree. In nineteenth-century Britain, railway journeys helped turn local time into a shared coordination problem, while the telegraph helped distribute an answer.

5–7 min

When Britain’s railways needed a shared clock

History5–7 minA timetable becomes awkward when the clocks at its two ends disagree. In nineteenth-century Britain, railway journeys helped turn local time into a shared coordination problem, while the telegraph helped distribute an answer.

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