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Updated: May 3, 2025


He is practical; he likes mathematics; he can talk to you from the binomial theorem up into Calculus; he is never so happy as when the air is buzzing with a conversation charged with induction coils, alternating currents, or atomic energy. The whole swing and force of popular science is his kingdom. I will say for Hobart that he is just about in line to be king of it all.

To the Binomial theorem, previously discovered by Newton, Taylor now added, in his "Method of Increments," the celebrated theorem that bears his name. This was in 1715. The Calculus of Partial Differences was introduced by Euler in 1734. It was extended by D'Alembert, and was followed by that of Variations, by Euler and Lagrange, and by the method of Derivative Functions, by Lagrange, in 1772.

He spends his nights, not in social dissipation, but in gathering in rats, mice, flying-squirrels, and also birds. When he first brought me a bird, I told him that it was wrong, and tried to convince him, while he was eating it, that he was doing wrong; for he is a reasonable cat, and understands pretty much everything except the binomial theorem and the time down the cycloidal arc.

"I don't feel up to anything to-day." "Then everything is lost!" I thought to myself. Instead of the brilliant result which I had anticipated I should be for ever covered with shame more so even than Ikonin! Suddenly, under the very eyes of the professor, Ikonin turned to me, snatched my ticket out of my hands, and handed me his own. I looked at his ticket. It was Newton's Binomial!

Next day, my pupil is there. Blackboard and chalk, everything is ready. Not quite so ready is the master. I bravely broach my binomial theorem. My hearer becomes interested in the combinations of letters. Not for a moment does he suspect that I am putting the cart before the horse and beginning where we ought to have finished.

There are many things in the "eternal womanly" which men understand about as well as a kitten does the binomial theorem, but some mysteries become simple enough when the leading fact is grasped that woman's song of life is written in a minor key and that she actually enjoys the semblance of sorrow. Still, the average woman wishes to be idealised and strongly objects to being understood.

He spends his nights, not in social dissipation, but in gathering in rats, mice, flying-squirrels, and also birds. When he first brought me a bird, I told him that it was wrong, and tried to convince him, while he was eating it, that he was doing wrong; for he is a reasonable cat, and understands pretty much everything except the binomial theorem and the time down the cycloidal arc.

It is a question, not of miracle, but of evolution, of growth. Newton had to master the multiplication table, then the four rules of arithmetic, then the rudiments of algebra, before he came to the binomial theorem. At each point, there was attention, concentration, insight; until these were attained, no progress to the next point was possible. So with Darwin.

It never seems to occur to the teacher that the pupil of the third grade might give the words of the binomial theorem without the slightest apprehension of its meaning. We grade for the repetition of words, not for intelligence.

It would be better from this point of view to endeavor, as has been suggested, to render this formula more exact by the substitution of a fractional power in the place of the square, rather than to go through the long calculations necessitated by the use of the binomial au + bu squared. Accordingly, making use of the formula b1 u squared, the above equation becomes,

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