Chessboard paradox

High school (ages 12+)
Mathematics & Numbers

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Date:

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/chessboard-paradox

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. How big is Chessboard paradox?Apparent increase from 64 to 65 square units
2. What is the paradox classification?Falsidical paradox based on geometric optical illusion
3. What is the attributed individuals?Sam Loyd (puzzle inventor, 1841–1911) and Oskar Schlömilch (mathematician, 1832–1901)
4. How does the chessboard trick make the rectangle look bigger?The trick works because the cuts create tiny gaps along the diagonal of the rectangle. These gaps are so small that our eyes think the rectangle is a perfect shape.
5. Why does the rectangle seem to have more area than the square?The rectangle appears to have more area because the gaps along its diagonal make the rectangle look a little bigger, even though the total area of the pieces is the same as the original square.

Falsidical Paradox: A paradox that appears genuine but is resolved by a flaw in its premise or a misinterpretation of visual data.
Optical Illusion: A perception that deviates from objective reality, often due to the way the brain processes visual information.
Geometric Dissection: The process of dividing a geometric shape into smaller pieces.
Slope: The measure of the steepness of a line, indicating its rate of rise or fall.