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I'm sure other folks have figured out the following, but just in case . . . .

Suppose you want to slice a board into six equal strips.  You need to lay out the dividing lines.  The board is almost eight inches wide, but it's an eighth of an inch shy.  In other words, its width is 7 and 7/8 inches.

How can you divide 7 and 7/8 six ways?  Remembering what you learned in elementary school, you have to begin by converting it to 63/8 inches.  But 63 is not divisible by six.  If you double both numerator and denominator, the fraction becomes 126/16 inches, and 126 is divisible by six.

So you decide to use 16ths of an inch.  You get out your ruler and mark off five dividing points as follows:


D I S T A N C E    F R O M    E D G E

Sixteenths of an inch








Inches and sixteenths


1 and 5

2 and 10

3 and 15

5 and 4

6 and 9


Make a mark at








That's a lot of arithmetic.  A couple of tricks will make your task easier.

First, avoid the fractions by going metric.  Your ruler measures 20 centimeters straight across the board.  It's simple to divide 20 by six; the result is 3.33 cm per strip.

That number is still somewhat awkward for making your marks, because dividing 20 by six doesn't yield a whole number.  But dividing 30 by six does.  That suggests the second trick:  Rotate the ruler (in this case, by 48°) until it measures 30 cm diagonally across the board.  Then you can simply make your marks at 5, 10, 15, 20, and 25 cm.


OCT. 27, 2014   HALLOW-EEK

You’re probably familiar with the phrase “eke out a living.”  Eke, pronounced “eek,” is a verb that means “to achieve with difficulty.”

There was once a different English word also spelled eke, except it was an adverb and was pronounced “ache.”  Like the German auch, this eke meant “also.”  William Shakespeare sometimes used it.  Geoffrey Chaucer eke employed it two centuries earlier:

Whan that Aprille with his shoures soote
The droghte of Marche hath perced to the roote . . .
Whan Zephirus eke with his swete breeth
Inspired hath in every holt and heath . . .

Mickey Rooney’s passing earlier this year prompted me to watch his 1935 appearance in the film of Shakespeare’s A Midsummer Night’s Dream.  Comic actor Joe E. Brown eke was in the movie, playing the character called Flute.  In Act III, he had a punning line describing the young Pyramus:  “most brisky jew-venile and eke most lovely Jew.”

“And eke”?  There are alternative possibilities like “and also” or “and at the same time” or “as well as.”  However, those would not have fit the iambic meter, so Shakespeare chose “and eke” though the word had already begun to fade into obsolescence.  (He also spelled the preceding word “juvenal.”)

But Joe E. Brown must not have been familiar with Middle English vocabulary.  He knew not eke (“ache”), but only eke (“eek”) as in “Eek! A mouse!”  The actor raised his pitch and squeaked the word as “eek!”  The meaning seemed to be “most animated juvenile and — horrors! — most lovely Jew.”  I cringed slightly.

Welp, this week is a scary one.  We might call it Halloweek.  Many will be cringing and shrieking “Eek!” in the Flutish sense, even in Pittsburgh.

Way back in the haunted Victorian era, just three miles down the Allegheny River from where I live now, the Pittsburgh Plate Glass Company opened its first factory in 1883 on the sandy banks of Creighton, Pennsylvania.

Their name eventually shriveled to PPG, while their product line swelled to include Pittsburgh Paints.

In 1983 the hundred-year-old manufacturer moved to a new corporate headquarters (right), a complex of buildings in downtown Pittsburgh designed by famed architects Philip Johnson and John Burgee.  The office towers are sheathed in PPG glass, of course.  A plaza in the center features a 44-foot pink granite obelisk.

From eye level, one’s gaze is drawn to the ominous black balls at the base of the “monument” (above).  They inspired local columnist Peter Leo to dub it, unofficially, the Tomb of the Unknown Bowler.

Also in PPG Place until three weeks ago, looming over visitors were two huge dancers modeled after a Renoir painting (right).

And in season, a 60-foot Christmas tree will conceal the Tomb and will be surrounded by a skating rink.  

But the really imposing part of the complex is the 40-story office tower (below).  During a recent full moon, photographer Dave DiCello captured Pittsburgh’s creepy castle with its spooky glass spires.

Herewith, I wish you ghostly dreams and eke a happy Halloween!



Not just anyone can marry the daughter of a king.  He must be a valiant warrior, and he must purchase the beautiful maiden with a bagful of severed body parts.

My latest article revisits the story of The Princess.


OCT. 22, 2009 flashback   IT'S HALFTIME!

I have a plan that would solve two problems with postseason baseball.  All times are Eastern.

Problem one:  the Three Rivers Stadium effect.  That ballpark hosted the first night game in World Series history in 1971.  Since then, baseball’s "Fall Classic" has become an exclusively prime-time event, featuring titanic marathons that often are not decided until after midnight.  Last Saturday’s ALCS contest at Yankee Stadium (not even part of the World Series) wasn’t decided until 1:07 AM.  That’s well past the bedtime of many young fans.  Old-timers like me wonder why some Series games can’t be played in the afternoon, at least on weekends, as all the games were when we were kids.  Of course, the answer is money.  But we can dream.  The sun ought to shine on part of the Series.

Problem two:  the Koufax/Drysdale effect.  In 1965 the Los Angeles Dodgers had two ace pitchers, Sandy Koufax (26-8, 2.04 ERA) and Don Drysdale (23-12, 2.77 ERA).  Nowadays, two pitchers in a five-man rotation start only 40% of the team’s games.  Back then, Walter Alston used a four-man rotation and managed to assign 51% of the Dodgers’ starts to his aces.  And he gave them 71% in the World Series, as Drysdale took the mound for games 1-4 and Koufax for games 2-5-7.  The Dodgers won in seven games, demonstrating how — in a short playoff series with several off days — a team built around a couple of dominating starting pitchers has the edge over a team (in this case, the Twins) that might have been better during the everyday grind of the regular season.

My plan:  schedule some World Series games as split day/night events.  Each ticket consists of two parts, one for the day session and one for the night session.  A fan might choose to attend only one session and give the other half of his ticket to someone else, someone who might not otherwise have been able to see the Fall Classic in person.

The on-field ceremonies commence at 1:30 in the afternoon.  Network TV coverage begins at 2:00 with a quick preview of the matchup, and the first pitch is thrown at 2:08.

At the conclusion of the fifth inning, maybe around 4:30, it’s halftime!  The grounds crew goes to work as if it were a rain delay.  The players leave the field, the network signs off, the fans leave the ballpark, and everyone has a nice supper.

If a Koufax or a Drysdale started the game, they’ve thrown five innings, enough to qualify for a win.  But now they have to cool off during a long halftime break.  The way pitchers’ arms work, they won’t be able to go back out there tonight.  Someone else will have to take the mound for the sixth inning.  The pitching duties are spread around the staff, thereby lessening the unfair advantage of the Koufax/Drysdale effect.

Network coverage resumes at 8:00 with highlights of the first five innings.  Celebrities are introduced, the National Anthem is sung, and lots of prime-time commercials are aired.  The sixth inning begins at 8:38.

Assuming the game is a typical five-hour World Series struggle, it should be over before 11:30.



“I am at a loss for an explanation, Detective.  The crime took place within this room.  However, the room was locked all night.  Therefore, what happened is impossible.  It could only have been an act of God!”

“I have no need of that hypothesis.”

An ancient locked-room mystery and an ancient courtroom drama are both part of my latest Biblical re-imagining, which is called The Jig Is Up.



For doing well on some math test when I was a student at Richwood High School, I was awarded the golden lapel pin you see below.  It depicts the Mathematical Association of America's iconic icosahedron (20 faces) over a nonagonal background (nine points).

Thirty miles to the southeast, a dozen Democratic Presidential hopefuls held a big debate last night.  I wasn't watching, but I understand that one candidate, Andrew Yang, had a numbers-based pin of his own.

His political numbers aren't encouraging; today's Economist poll shows him in seventh place with only two per cent support.  But his pin promotes MATH.  Mr. Yang says that's an acronym for Make America Think Harder. 


OCT. 15, 2019    WOMAN IN THE MOON

When we humans first dared to travel a quarter of a million miles away, nothing humbled us more than looking back at the small, vulnerable place from which we had come.

Of an even more distant image, Carl Sagan wrote, “That's home.  That's us.  On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives.  ...There is perhaps no better demonstration of the folly of human conceits ... [and] our responsibility to deal more kindly with one another and to preserve and cherish the pale blue dot, the only home we've ever known.”

But a similar image had already thrilled humans four decades earlier.  It appeared in a motion picture that opened ninety years ago today!

See my article about the woman and her friends who traveled to the moon, Frau im Mond.


OCT. 14, 2009 flashback   A BIT OF FICTION  (EDITED 2019)

Buzz the engineering student was home for the weekend.  His cousin, still in high school, invited him to the homecoming football game Friday night at Ourtown High.

“You’ll have a blast!” Cuzz enthused.  “They’ve installed all new seats in the stadium, and I can get us a spot front-row center!”

When they arrived at the field, Buzz had to admit the refurbished stadium looked good.  On both the home and visitor sides, there were twenty rows of seats between the 30-yard lines.  Buzz did a quick calculation and estimated the maximum capacity at about 3,600 fans.  It was hardly the Rose Bowl, but it was the perfect size for their high school.

Cuzz was true to his word.  He led his cousin to two seats on the home side of the field, and they were in the very front row.

“Couldn’t we see better,” Buzz asked, “if we were up higher?  How about those seats back there?”

“Nah,” Cuzz scoffed, “the upper half is the parents’ section.  Old folks sit up there.  We’re down here, right in the middle of the action!”

“Pretty close to it, anyway,” Buzz admitted.  But he had an engineer’s compulsion for precision. “Actually, we aren’t exactly in the middle.  We’re on the 44-yard line.  Those kids eight seats to our right, they’re on the 50.”

“But this is plenty good enough.  Look, you can almost lean forward and touch the players.”

It was true.  The front row was unusually close to the sideline, though five feet higher.  The wall was padded for the players’ protection, all the way up to the railing in front of the fans.  When a player stood behind the bench, Buzz and Cuzz could have kicked his helmet if not for that padded wall.

In most stadiums, the cheerleaders would have been deployed between the bench and the stands.  But there was no space for them here; the players claimed the whole sideline between the 35s.  The cheerleaders split into two groups, Left-End and Right-End.  They stood on the sideline near each 30, where the seating section ended. “They’re going to be lonely down there,” Buzz thought.

The teams took the field for the kickoff.  Ourtown High would receive and defend the goal to the left.

In Buzz's section, gates closed to block off the entrances, and he felt his seat shudder slightly.  At first he thought the fans were standing up in anticipation of the start of the game.  But no, his seat and 900 others were actually moving to the left!

“What’s going on?” he asked.

“Didn’t I tell you this was going to be great?” Cuzz replied.  “We’re dropping back to receive the kickoff!”

Buzz realized that their half of the home section was on rails, and an electric motor was trucking it to the left at two miles per hour. 

Across the way, the lower half of the visitor section was also on the move.

The kickoff was returned to the 19-yard line, and when the seats came to a stop after about half a minute, Buzz and Cuzz were sitting on the 18!  They were as close to the action as the head coach was.

Ourtown methodically moved the ball down the field, and with each play the section of seats followed along at one yard per second, always centering itself five yards beyond the ball. 

That meant that when Ourtown was on offense in the first quarter, Buzz and Cuzz found themselves just one yard behind the line of scrimmage, alongside the wideouts.  When the visitors took over and started driving from right to left, their seats were now eleven yards ahead of the line, alongside the safeties.

Ourtown got the ball back and completed a 40-yard pass play down to the 6.  The seats traveled much slower than the receiver — “They aren’t allowed to go any faster, because of safety,” Cuzz explained — but they had almost reached their new station by the time the next play was run.  The Right-End cheerleaders welcomed the fans’ arrival, then turned to cheer the Hometown touchdown.

“Wasn’t I right?” Cuzz shouted over the din.  “Aren’t these seats great?”

Buzz had to admit they were.  “Whose idea was this, anyway?”

“Oh,” said Cuzz, “I think Coach heard about it several years ago.  It was on a website page by some guy named Tom Thomas.”




Some kids threw Frisbees.  I threw a yardstick, kept aloft by the Magnus effect beneath the blooms and beans of the spreading catalpa tree.  I also photographed the trunk of the tree, viewing the photos with a stereoscope made from Tinker Toys.

All of this, plus the introduction of the new 1955 Farmall tractors, somehow made it into this month's 100 Moons article.



I've written before that unfamiliar large rooms frighten me.  Since childhood, I've been scared to look up towards a high ceiling.  In such situations, I cringe.

I seemed to fear that tilting my gaze upward would cause me to lose sight of the “horizon” (the bottom of the wall) and lose my balance.  What happened to the floor?

I've been afraid,” I wrote, “I'd fall down and go boom.  My toes curl downward in a vain attempt to grip the floor more tightly.”

Perhaps cringing is a symptom with more than one cause.  Noting that humans likewise tend to duck when we hear nearby thunder, I speculated that our species had learned “the safest response to lightning is to lie flat, hugging the ground with your hands and your toes, so that the lightning strikes not you but something taller like a nearby bush.  ...Evolution would have eliminated (by electrocution) any humans who did not react properly to a thunderstorm.  Similarly, there are few dogs left that do not fear thunder.”

However, I continue to ponder my vertiginous fear of toppling.  Now that I'm a somewhat weaker septuagenarian, I cringe even more because I perceive myself as less steady on my feet.

Yes, I am a cautious chimpanzee.  (It's more evidence that humans have evolved from apes.)

Both my feet grasp the branch more tightly.

To keep my balance, I reach out with at least one arm.  If I can't touch another branch or a wall or a piece of furniture, a cane can help.


OCT. 7, 2009 flashback   WHERE HAVE ALL THE COLORS GONE?

As an member of AAA, I recently was e-mailed a little feature claiming to describe “What Your Car Color Says About You.”

While there are a wide variety of shades, here are some basic messages each color conveys.


Empowered; not easily manipulated. Loves elegance, appreciates the classics.




Sexy, speedy, high-energy and dynamic.

Dark Blue

Credible, confident and dependable.

Light to Mid-Blue

Cool, calm, quiet.


Elegant, futuristic, cool.

I currently drive a blue sedan, and both of the “blue” descriptions fit me.  But my previous car was dark red, and I definitely am not a stereotypically aggressive red-car driver.

I’ve also owned a green car and a gold car.  Where are those hues?  And where are other possibilities, like purple and orange and yellow and brown and pink and turquoise?  Those were available when I was growing up in the Fifties.

As late as 1994, green was the most popular color.  Now, not so much.

When I look at a parking lot, such as this one in front of the Marine Terminal at LaGuardia Airport, I see shades of gray (black, white, silver) interspersed with a little red.

PPG Industries confirms my observation.  The paint company reports that silver has been the No. 1 color for nine straight years.  It now accounts for 25% of vehicle paint choices in the United States.  White and black get 18% and 16% respectively, while red is in fourth place with 12%.

Apparently most drivers have become “elegant and fastidious” and only one in eight is “speedy.”  That does not square with my actual experiences on the highway, but color choices don't lie, do they?

10-YEAR UPDATE (2019)

PPG says the proportion of cars with no hue has increased from 63% to 76%.  The favorite is now white, on 26% of vehicles in North America (and 39% globally).

A reader of the Click & Clack column asked why.  "My second car," he wrote, "was a two-tone copper and cream 1956 Bel Air.  What happened?  Why are our colors so boring and washed out?"

The reply from Car Talk's Ray Magliozzi (left):  "The answer is fashion.  Fashion is something that's so ridiculous that we have to throw it out every six months and start all over.  But when you're buying a house or a car, you're likely to feel more risk-averse.  So people tend to stick with (a) muted colors and (b) colors that lots of other people have already chosen, because that makes them feel that they're making a safe choice."



At the end of September, 1869, Probate Judge W.T. Sinclair of Monroe County, Ohio, granted a marriage license to two teenagers:  John Thomas Buckingham, then employed by Captain Thomas Hughes at his store in Stafford, and Mary E. Curtis.  They were legally united as husband and wife on October 5 — exactly 150 years ago today!

The new couple made their home four miles northwest of Stafford, on a hill known as Curtis Ridge (presumably after Mary's family).

On their farm, "Tommy" and Mary raised four daughters and a son.  The son was named Harry Gladstone Buckingham.  That's him in the middle, growing up.

At age 28 Harry would have a daughter, and she would grow up and have a son at age 34, and that would be me!

Yes, Tommy and Mary Buckingham were my great-grandparents.  I'm 72 years old now and my ancestors are long departed, but a gift for their 150th anniversary seems appropriate.

However, traditional gift lists only go as far as the Diamond Anniversary, after 75 years of marriage.  What about 150 years?  Should it be the Double Diamond Anniversary?  Should it be Triple Gold?  Or is there some other precious material associated with the sesquicentennial number 150?

Well, as a former physics major I'm aware of a certain rare-earth metal used in magnets.  It has an approximate atomic weight of 150.  Therefore, I hereby declare today to be Tommy and Mary's Samarium Anniversary!



In the past, baseball fans would grab the newspaper when it arrived each day.  They'd turn first to the sports page to check the standings.  “How's my team doing?”

In the present, the Pittsburgh Post-Gazette no longer arrives each day.  It's still online, but currently there are only three print editions per week.

Nevertheless, any of my fellow ’Burghers following the local team this spring must have been elated for the five days in April shaded below in blue.  The Pirates, with 12 wins and only 6 losses, were in already in first place in the National League Central Division!

However, 142 games still lay ahead.  Late in April there was a slump.  Early in June there was a deeper slump, shown here in red.  The Pirates were in last place for a while, indicated by the green shading.

But after June 13 they put together another .667 run (14-7).  Local fans remained hopeful.  In the first five games of July, Josh Bell hit five home runs!  He went 8 for 19 with 14 runs batted in!  A few days later, he was in the All-Star Game!  More to the point, our team's record at the break, shown above in gold, was 44-45.  We were within striking distance of first place, only 2½ games out.

Then came disaster.  The second half of the season began with a .143 crash (4-24), also shown above in red.  The first nine of those losses dropped the Pirates permanently into last place.  By August 11 they were 15½ games behind first, and they would finish 22 games out.  (Actually, that was the closest divisional finish among the six cellar-dwelling teams; the Tigers ended up a disheartening 53½ games behind the Twins.)

Pittsburgh's 69-93 final record was not only a 13-game drop from the year before, it was the franchise's worst mark of the decade.  On the left, we see how the game-by-game results could be charted as a Diamond Brick Road.

Among the details of what went wrong:  Our fielders led the National League with 21 errors.  Our batters hit the NL's second fewest home runs.  Our pitchers posted the NL's second worst earned run average, and they set a modern-day franchise record by 31 times giving up ten or more runs in a game.  In our 93 losses we were outscored 692-290; that's more than 4.3 runs per game.

Nor was the home-game gate great.  For September 4 only 9,043 tickets were sold and most went unused, as Jason Mackey of the P-G showed us in this view from the pressbox shortly before the first pitch.

Two weeks later, the paid attendance was 10,933, but visiting comedian Craig Gass (who's learned to “count a house”) reported that just 600 fans actually showed up.

The following week, I myself went to PNC Park to work the Chicago Cubs' next-to-last telecast on WGN.  After 72 seasons the station will no longer have broadcast rights; the Cubs will produce the telecasts themselves.

On the left are some of the WGN directors and producers with whom I worked over the years when they came to Pittsburgh: Arne Harris (who died in 2001), Jim Holly, and Marc Brady.

Mark Vidonic commented, “This truly is the end of an era.  Countless of us had a special connection with the Cubs, Braves and Mets because of the superstation status of WGN, WTBS and WOR/WWOR.  There was always something special and magical about getting those stations on your cable.  Yes, you can now watch any team you want if you subscribe to the MLB.TV service, but it's not the same.”


Oh, well.  After the season-ending game on Sunday, Josh Bell tossed some leftover caps to a few diehard supporters.  As Alexander Pope remarked, “Hope springs eternal in the human breast; man never is, but always to be blest.”

Only 133 more days until pitchers and catchers report.   

Matt Freed, Post-Gazette