We staid till, it being darkish, we saw the fire as only one entire arch of fire from this to the other side the bridge, and in a bow up the hill for an arch of above a mile long: it made me weep to see it. The churches, houses, and all on fire and … Continue reading Cycloid


Austin TX Some people have favorite numbers. According to a global online poll, 7 is the world’s favorite. I admit I fancy 7, maybe because I have 6 siblings or because seven ate nine. Either way, there is a number I fancy more than 7. The number e has made an appearance in previous posts[1], most recently … Continue reading e

Euler’s Formula

Austin TX 2013/06/16 This post and the previous are sort of farewell gifts to my students who just finished their first year studying calculus. I love creating lectures (as you might imagine), but they hungered for something else. They challenged, inspired, and reminded me what I love about teaching. For me, the gift of teaching is … Continue reading Euler’s Formula

Taylor Series

This post was in the works for over a month. The chalk happened in one evening, but the research and writing took time. Taylor series make for a meaty topic, and Brook Taylor had a full life. Plus, infinity took me on a few tangential journeys. The big idea here is approximation, in particular the evolution … Continue reading Taylor Series