Walnut Math

Math Online Tom Circle

A friend from China gave us a bag of walnuts plucked from their home-grown walnut tree. I decide to count them by applying math:

A stack of walnuts piled in a pyramid, with base layer 6×6 walnuts, above layers 5×5, 4×4, 3×3, 2x 2, and finally top 1 (1×1).

How many walnuts are there in total ? (Answer: 91)

This is simple math but only taught in A-level (with proof by induction).

image

Hint: Watch free Khan Academy Math lecture to learn more ….

$latex displaystyle boxed {
sum_{1}^{n} k^2 =frac { n (n+1)(2n+1)} {6}
}$

This is a 400-year-old walnut tree: walnut is called “Wise fruit 聪明果”, it looks like human brain, also has proven nutritious benefits to brain.

image

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About tomcircle

Math amateur
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