STRANGE BUT TRUE- Sun sums: How to calculate shadow lengths

Q. On which day of the year does a house cast its longest shadow, and why might some folks want to know? –J. Tolbert

A. Sunshine access is the issue. Shadows are longest on the shortest day of the year, which is the winter solstice (in the Northern hemisphere about December 22), say Jeffrey Bennett and William Briggs in Using and Understanding Mathematics. Some cities have laws prohibiting property owners from constructing new houses or additions that cast shadows on nearby houses, thereby "allowing everyone access to the Sun for the use of solar energy devices." One such law prohibits structures casting a noontime shadow reaching farther than would be cast by a 12-foot fence on the property line, on the shortest day of the year. Hmmm– always wondered when those trigonometry tables would come in handy.

Q. Special birthdays such as the first, 21st (adulthood), and 100th (centenarian) are common, but around the world, what are some uncommon special ones? –W. Scott

A. Japan: 60, 69, 76, 77, 87, 89, 98 are traditional celebrations of longevity ("chojuiwai"). Ages 3 and 5 for boys and 3 and 7 for girls are also considered significant. (University of Hawaii's Center for Japanese Studies) In China, 30 signals adulthood. And in several Latino cultures, a girl's 15th birthday (a "quinceanera") marks this passage.      

Many African cultures have coming-of-age parties in groups rather than for individual children, much like certain Lutheran or Catholic confirmation ceremonies. Northern Germany: A man still without a wife on his 30th birthday sweeps the stairs of city hall to show he's available and not a bad bargain since he cleans house well. An unmarried woman polishes her front door knob.            

Northern Europe: Birthdays 10, 20, 30, 40, etc are much-gifted "round" years, says University of California-Los Angeles folklorist Timothy R. Tangherlini. Vietnam: Tet, the start of the lunar New Year, is considered everyone's birthday. Babies turn 1 on Tet no matter the exact day they were born.

Korean babies are "1" at birth and turn a year older on lunar New Year's, adds Tangherlini. "Tol" is celebration of the first anniversary of the birth, so a child born right before lunar New Year might be considered "2 years old" from day 3 through the next New Year. 60 is most significant, marking a full zodiacal cycle and a full lifetime– "Anything after that is icing on the cake."

Q. Could a person live without a stomach? –K.Moss

A. As a child, Mike S. watched his mother, aunts, and uncles die of stomach cancer, and as an adult he lived in dread of the disease, to the point where he never married, says Amy Adams in Stanford Medicine magazine. Then in recent years, Mike and others in the family were tested and found to be carriers of a rare cancer-causing mutation, putting them at 70-80 percent risk of getting the killer disease. 

They eventually decided "their best defense was offense" by having their stomachs removed and the bottom of the esophagus attached directly to the intestine. While this is major surgery, 11 of the cousins went ahead with the procedure. 

"The specter of gastric cancer is gone forever," Mike says now. 

But patients need a new way of eating afterward. Some foods such as salads take a long time to digest and fall off the menu; others are okay in small quantities. One patient says she can still eat almost anything, as long as she remembers to "chew, chew, chew."

Q. Six beefy guys line up on one side, six on the other, 1800 pounds v. 1800 pounds, the total kinetic energy unloosed by each "wall of bodies" during the collision equivalent to a 1.5-ton pickup truck going 4.3 mph, or to 6 bullets from a .357 Magnum handgun. And it's not just hit on hit, force = ma, but also body leverage and torque. Who are these big bruisers, and what's going on here? –T. Barber

A. They're the dozen or so offensive and defensive linemen going at one another during pro football action, says Timothy Gay in Football Physics: The Science of the Game. Actually, over an entire play of 5 seconds, each lineman could deliver 4.3 horsepower. Total kinetic energy estimated for all players on both sides is a whopping 40,000 horsepower-seconds for a game of 100 plays, or enough to lift the 1.5-ton pickup truck 87,000 inches into the air, or 1.4 miles!

Interestingly, says Gay, because of a 60 percent increase in player weight and 12 percent climb in top-speed since 1920, total kinetic energy dumped into "the pit" has likely doubled, yet major injuries (concussions, broken legs) have stayed about the same, primarily owing to better equipment.

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