XY-Coordinate System Symmetry with Examples

Logic, Mathematics
[caption id="attachment_28582" align="alignright" width="480"] Image Department of Energy[/caption]In high school mathematics, the topic of symmetry is bound to arise. Especially is this so in analytic geometry. For curve C, what is its XY coordinate system symmetry? How is it symmetric about the y-axis? The x-axis? The origin? The line y = x? The line y = -x? Symmetric about some point other than the origin? Symmetry About the Y-Axis Symmetry about the y-axis means that if there is a curve that lies to the right of the y-axis, there is an identical copy of it to the left of the y-axis. That is, it is symmetrical if each x value can be replaced with –x. Thus, the parabola y = 1/2x2 is symmetric with regard to the y-axis. For every…
Read More

Devils Dice – What Are They?

Chemistry, Geology
[caption id="attachment_13950" align="alignright" width="380"] Peruvian Striated Pyrite - Rob Lavinsky iRocks.com CCSA3.0[/caption] I was in my 30s when I first heard of Devils Dice. What are they? I was raised in New Jersey. At the age of 33, I moved to Virginia. This short north-to-south emigration exposed me to certain speech, food, and culture changes. It took me a month to get over the accent. During that time, my brain adjusted and the accent sounded totally normal to me! I missed scrapple a lot. Since then, I’m happy to say scrapple successfully has invaded the south. But there were other changes as well. In the south, there are buzzards. There are red bud trees. There are ABC stores! Even the ground itself offered something new. There is this kind of…
Read More

Cubane: The Chemist’s Toy?

Cubane is an organic hydrocarbon. It consists of carbon and hydrogen and is cubic in shape. It is a very curious substance, indeed. With no practical purpose in view, it was first prepared in 1964. There is an endless number of theoretical molecular possibilities in the world of organic chemistry. Some chemicals are simple. Others are complex. Some are of practical use to mankind. Some are mere toys of the intellect. Yes, adults must have their toys! Cubism "We do the difficult immediately. The impossible takes a little time." Chemists enjoy challenges. One challenge was to synthesize cubane (C8H8). It is a cut with a carbon atom at each corner. Attached to each of them is one hydrogen atom (see the image). Now carbon "prefers" to form angles of 109.5…
Read More