Cauchy's integral formula

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/cauchy-s-integral-formula

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the discoverer?Augustin-Louis Cauchy
2. What is the year of publication?Circa 1831
3. Why is Cauchy's integral formula called a magic trick?It’s called a magic trick because it shows that knowing the function on the outside of a shape can reveal exactly what happens inside, like a treasure map.
4. How does the formula help find values inside a shape?The formula says that if you take all the points around the loop, divide the function’s value at each point by how far that point is from the inside point, and add them up, you get the inside value times a special number (1 over 2πi).

Analytic Function: A complex function that is differentiable at every point in an open set.
Contour Integral: An integral taken along a curve in the complex plane.
Simply Connected Domain: A region in the complex plane where any closed loop can be continuously shrunk to a point.