Bernhard Riemann and the Geometry of Curved Space
Draw a triangle on a flat sheet of paper, and its three angles add up to 180 degrees. Now imagine drawing a triangle on a globe. Could its angles add up to more than 180 degrees? They can—and that surprising difference points toward a way of thinking about geometry that mathematician Bernhard Riemann helped develop.
Riemann was born on September 17, 1826, in the village of Breselenz, in what is now Germany. He grew up in a pastor’s family and showed an early talent for mathematics. His work eventually reached far beyond the shapes studied in ordinary school geometry. He asked how people could describe spaces that curve, including spaces with more dimensions than the surfaces we can easily picture.
A different kind of triangle
To see why curved geometry raises new questions, picture a globe with a grid of lines running around it. The equator circles the middle, while lines of longitude run from the North Pole to the South Pole. These lines are curved when viewed from outside the globe, but they can serve as paths on its surface.
- curvature:
- The way or amount a surface or space curves.
- counterparts:
- Things that have similar roles in different situations.
- approximately:
- Close to an amount or description, but not exact.
- independent:
- Separate from and not dependent on something else.
- foundations:
- The basic ideas on which a subject is built.
- framework:
- A structure of ideas used to study or understand something.
- influence:
- An effect on how someone thinks or works.
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Preview questions from this passageShowHide
- 1Why does the article begin by comparing triangles on paper and on a globe?
- 2How does the globe triangle show that the flat-triangle angle rule depends on the surface?
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About this explanatory article passage for Middle School
“Bernhard Riemann and the Geometry of Curved Space” is a explanatory article reading passage about Geometry of curved space, written for Middle School. It takes about 7 minutes to read (981 words) and comes with an interactive quiz and a printable worksheet with comprehension questions and an answer key.