On a moonlit stroll, a young man points to the cloudless sky and says, “Look—a full moon!”

His date is not impressed. “Technically,” she replies, “the Moon’s not full until 2pm, when its ecliptic longitude is opposite to that of the Sun.”

Hoping to save his pride, he replies, “But the Moon looks completely illuminated.”

“It’s never one hundred percent illuminated,” his date says, unfazed. She’s a tough cookie. “Oh, and on this side of the world it’ll be a corn moon.”

Pretending to check his watch, the young man gets confused. He remembers his science teacher explaining that the Moon reflects sunlight and that it is full when it is on the other side of the Earth from the sun, but the nighttime half of the Earth is on the opposite side of the Sun, so how could that be 2pm? Did the newspaper say it would be a full moon tonight, or did it say tomorrow night? And what’s a corn moon?

There’s only one thing he can do: look it up on Wolfram|Alpha!

One of the latest features added to Wolfram|Alpha is more coverage of full moons and other Moon phases. Back when people got their information from only a local newspaper, it was relatively simple to say that one night or another would be a full moon, because for a specific location, the time of a full moon would be closest to midnight on that day. But now it is easy to get your information from a newspaper that is far away, so its date can be off by a day. Of course, Wolfram|Alpha detects your location, so it is able to predict the date of the next full moon in your area, and the “Precise time” button reveals the exact time the full moon will take place.

Remember that because of time zone differences, there is always part of the world that is on a different day. And that affects labels like “corn moon”, which is the first full moon in September. The beginning and ending dates of September depend on the time zone, and sometimes the full moon is close to this boundary. The next ambiguous corn moon will be in 2012. More »

Consider packing circles inside a circular container, or less abstractly, placing cookie dough on a cookie sheet. In the case of cookies, which expand to be a roughly circular shape, you don’t want them so close that they run into each other. At the same time, you don’t want them too far apart, because that would mean fewer cookies.

One of the latest features of Wolfram|Alpha is the ability to get information about packing circles into circles.

For instance, suppose you have a circular baking sheet with a diameter of 12 inches, and you want to make 20 cookies. You can ask Wolfram|Alpha “pack 20 circles in a diameter 12 inch circle”; not only does it give you a diagram of the densest packing, but also the largest radius of the circular cookies on the 12-inch baking sheet.

Or you might know the size of the cookies and want to know how many can fit? One way to get the answer would be “pack r=1 circles in a diameter 12 circle”.
More »

Every day the Sun crosses the sky, rising in the east and setting in the west, but in detail its path is different every time. If it is winter, or if you live in the north, the Sun is lower and stays closer to the southern horizon. While the time of year and the location have similar effects, they act independently on the overall path. The Sun’s path is unique for your place and time.

You can see the sunpath today at your location; the default is the perspective of looking toward the southern horizon.

The autumnal equinox is tonight (in North America), but in Pyramid Point (a place close to the equator in the Pacific), the equinox will occur Thursday, close to noon, when the Sun will be almost overhead. More »

One thing that is full of confusion is figuring out relationships. It can also be full of surprises, like the fact that Wolfram|Alpha can do it for you. If you follow this blog, you already know that Wolfram|Alpha can figure out and calculate lots of different things, including the moon and planets, and you are about to discover what it can tell you about your relationships.

Or at least relationships between your relatives. For instance, my cousin just had a son”.

We get a family tree, and it tells us that my relationship to my cousin’s son is that he is my first cousin once removed. Confusion resolved.

Like many other Wolfram|Alpha outputs, we get more than we may have expected. A few genealogical properties are related to historical laws, and a few are biological. The plots for sharing a Mendelian trait are given at the bottom after clicking More. This helps me understand how much I may have in common with my new first cousin once removed.

A dominant trait only requires one allele, while a recessive trait requires two. The other piece of information needed to say how likely it is to share a trait is how common it is in the general population. It is possible to share a trait accidentally, and for recessive traits one needs to get the other allele from the other parent. For my cousin’s son, not surprisingly, we see that the probability of sharing a genetic trait in common doesn’t seem to depend much on whether it is dominant or recessive. We are too distantly related to have much in common, and the probability of a shared trait between us depends primarily on the chance coming from the frequency in the general population.

It turns out that most traits are not simple like this, and involve more than one gene and so on, but this gives a general sense of how much we may have in common.

You probably know people who get confused about second cousins and so on, but there is also another category for relationship confusion. More »