I got my first taste of solid mechanics (and fracture mechanics) as a kid when attempting to use 'Number 2' pencils, on which I gave up rather quickly. Once they break once, they will soon break again. I switched to "mechanical pencils" (I like the .07 size) when I was very young.
Here is an old article on pencil-tip fracture (by Henry Petroski). The picture below, which comes from an even earlier article, sets up the the geometry of a pencil tip.
(I was thinking about this because a 'Number 2' pencil showed up in The Grimm Legacy, which I am currently reading.)
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