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Showing posts from October, 2016

Gauss's quote for positive, negative, and imaginary number

Recently I watched the following great videos about imaginary numbers by Welch Labs.

https://youtu.be/T647CGsuOVU?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF

I like this article about naming of math by Kalid Azad.

https://betterexplained.com/articles/learning-tip-idea-name/

Both articles mentioned about Gauss, who suggested to use other names of positive, negative, and imaginary numbers. Gauss wrote these names are wrong and that is one of the reason people didn't get why negative times negative is positive, or, pure positive imaginary times pure positive imaginary is negative real number. I made a few videos about explaining why -1 * -1 = +1, too.

Explanation: why -1 * -1 = +1 by pattern
https://youtu.be/uD7JRdAzKP8

Explanation: why -1 * -1 = +1 by climbing a mountain
https://youtu.be/uD7JRdAzKP8

But actually Gauss's insight is much powerful. The original is in the Gauß, Werke, Bd. 2, S. 178.
Hätte man +1, -1, √-1) nicht positiv, negative, imaginäre (oder gar ummögliche) Einheit, son…

Random quotes from ancient time to now

The quality measure of a city (country) is what it does with its referendum.
-- a philosopher
A good decision is based on knowledge and not on numbers.
-- Plato
Dictatorship naturally arises out of democracy, and the most aggravated form of tyranny and slavery out of the most extreme liberty.
-- Plato
One of the penalties for refusing to participate in politics is that you end up being governed by your inferiors.
-- Plato
Yes, he said; but what are the characteristics of this form of government, and what are the defects of which we were speaking? First of all, I said, consider the nature of the qualification just think what would happen if pilots were to be chosen according to their property, and a poor man were refused permission to steer, even though he were a better pilot?-- The republic, Plato