Well, they continue to introduce Pythagorean theorem through many stages of elementary math, so 8 is pretty early. But.. here could be a section of a textbook:

Pythagoras & The Pythagoreans: Mathematics, Music, and Mystery

Pythagoras was an ancient Greek mathematician and philosopher who lived around 500 BC. He traveled widely and gathered knowledge from diverse cultures, like Egypt. He also founded his own school of men and women in Italy. There, he taught that numbers held the key to understanding the whole universe. Pythagoras is best known for the Pythagorean theorem.

Fun Fact! There are stories that when Pythagoras discovered his famous theorem, he celebrated in a big way. Some say he sacrificed 100 oxen, while others claim it was just an ox made of flour. The Pythagoreans were famously vegetarian, so what do you think?

Math & Music: Pythagoreans explored the relationship between math and music. They discovered that musical notes have mathematical relationships. Hippasus, a member of the Pythagorean community, used bronze disks to show that musical notes are connected to mathematical ratios. This is considered one of the first scientific experiments!

Activity: Using a stringed instrument, like a guitar, try plucking the strings when pressing at 1/2 the string or 2/3s the string. Try different fractions. Can you hear the mathematical relationships in the sounds?

When I was 8 I would sometimes watch a Disney VHS tape that had Donald Duck exploring stuff like this. The golden ratio, octaves of sound/music, pythagorean theorem etc. I loved it.

Which is why hands-on learning combined with source material is best practice for children, imo. Taking several disks and demonstrating that the thicknesses double but diameter is the same, letting the kids try hitting them and noting the differences in tone.

Asking the children "why do you think these sound different?" without telling them why first, letting them explore it themselves, gently correcting them along the way. Then pulling out another example and encouraging them to apply the same logic to the new example.

No, instead for the most part, children _still_ get what we all had: memorise these facts without explanation and fill out the blank space on the exam where the memorised words get you points. Most of our entire schooling is just an exercise in memorisation, not in thought and it's sad.

They would be fascinated. I have one at home and a 12 yr old. This is the kind of stuff they’re always interested in.

They'd probably be fine.