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As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
In a way, this reinforces my hypothesis that Latin in traditional Western higher education was never quite so much about Latin itself as it was about gaining a deeper understanding and greater praxis of your native tongue by reading its source code.
Uhm, what? You couldn't be more off. Traditionally, any liberal arts education would include extensive familiarity with the classics. That means Plato & Dante, at the minimum, whether a BA or BS. You were expected to know Latin and Greek because you were expected to read Latin and Greek. If you were pursuing a BS, then perhaps you would read Euclid's "Elements" instead of Thucydides' "The History of the Peloponnesian…
Earlier quoted context omitted.
That isn't true. Only the history/geography was recall. Latin translation and geometric proofs aren't regurgitation.
Actually from a cursory look at the Latin part, it seemed that all of the sentences and things they chose for you to translate were very specific cases of applying rules. Maybe a bit harder than some of the other stuff, but still regurgitation.
> What is the reason that when different powers of the same quantity are multiplied together their exponents are added? As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
> What is the reason that when different powers of the same quantity are multiplied together their exponents are added? As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
Who here can come up with the most concise explanation?
X^N * X^M
= N copies of X, multiplied by M copies of X
= N+M copies of X multiplied together
= X^(N+M)> What is the reason that when different powers of the same quantity are multiplied together their exponents are added? As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
I feel like anybody with a basic understanding of what an exponent represents should be able to explain why you add exponents.
> What is the reason that when different powers of the same quantity are multiplied together their exponents are added? As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
Earlier quoted context omitted.
Who here can come up with the most concise explanation?
Me, me! Let me try! X^N * X^M = N copies of X, multiplied by M copies of X = N+M copies of X multiplied together = X^(N+M)
In a way, this reinforces my hypothesis that Latin in traditional Western higher education was never quite so much about Latin itself as it was about gaining a deeper understanding and greater praxis of your native tongue by reading its source code.
> What is the reason that when different powers of the same quantity are multiplied together their exponents are added? As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
Who here can come up with the most concise explanation?