This is the fifth of eleven Letters of Euler I will rewrite and post on the subject of infinitesimals (the infinitely small), an idea that is fundamental to a good understanding of calculus. Click here to read the previous letter. Letter XI. Reflections on Divisibility in infinitum, and on Monads. In speaking of the divisibility of body, we must carefully … Continue reading Letters of Euler to a German Princess, Vol. II, Letter XI
Leonhard Euler
Letters of Euler to a German Princess, Vol. II, Letter VIII
This is the second of eleven Letters of Euler I will rewrite and post on the subject of infinitesimals (the infinitely small), an idea that is fundamental to a good understanding of calculus. Click here to read the previous letter. Letter VIII. Divisibility of Extension in Infinitum The controversy between modern philosophies and geometricians to which I have … Continue reading Letters of Euler to a German Princess, Vol. II, Letter VIII
Letters of Euler to a German Princess, Vol. II, Letter VII
This is the first of eleven Letters of Euler I will rewrite and post on the subject of infinitesmals (the infinitely small), an idea that is fundamental to a good understanding of calculus. I am rewriting them from a 1795 English translation, and will edit some of the awkward character usage (among other things, the first "s" used in any … Continue reading Letters of Euler to a German Princess, Vol. II, Letter VII
It Only Takes an Instant
I never cease to be amazed by the technology of today's digital cameras. By pushing a few buttons, anyone crazy enough to bob around in a 6-8' high shore break can capture some amazing beauty in God's creation! But as the photos above reveal, the beauty only lasts for an instant. It seems impossible that things can … Continue reading It Only Takes an Instant
Weighing the Differences in 3rd and 4th Edition Saxon Algebra 1
Over the past few months, many parents have contacted us, asking if we plan to make a DIVE CD to teach the new Saxon Algebra 1, 4th edition textbook. The short answer is "no", and the short reason is that we believe the newer Saxon textbooks have strayed too far from John Saxon's (1923-1996) original, … Continue reading Weighing the Differences in 3rd and 4th Edition Saxon Algebra 1
Understanding vs. Memorization
A Google search of the phrase "understanding versus memorization" yielded some of the following comments: "The old style of teaching used to stress memorization." "More and more top-level research on how we learn backs up the benefits of 'teaching for understanding' versus memorization." "Productive thinking is defined as thinking based on an understanding of the nature … Continue reading Understanding vs. Memorization
Studying His Word and His Works 