Chipping Away at the Problem.

new pentagon 2_768 blog

Top left: The 15 types of pentagonal tilings discovered. Art: Ed Pegg/Wikipedia   Bottom left: The math.
Right: The 15th convex pentagon found to be able to tile a plane.  Art: Casey Mann

At Kowalski Heat Treating, we’re all about doing great work, constantly searching for new and better ways to help our clients grow their businesses – often rooted in problem solving your PIA (pain in the @#$) Jobs. And we marvel at new thinking and new discovery.

This week’s blog and email post salutes the work of three mathematicians in their discovery of the latest convex pentagrams to tile a plane, courtesy of a post by

Jennifer McLoud-Mann, along with her husband Casey and David Von Derau have spent the past few years trying to help unravel one of math’s long-standing unanswered questions. How many shapes are able to “tile the plane”? — meaning shapes that fit together perfectly to cover any flat surface without overlapping or leaving any gaps. For example, mathematicians have proved that all triangles and quadrilaterals (shapes with four sides), can tile the plane, and have documented all of the convex hexagons that can do it. But what about five sided pentagrams.

When dealing with pentagons — specifically convex, or nonregular pentagons with the angles pointing outward – the number of convex pentagons is infinite — and so is the number that could potentially tile a plane. It’s a problem that’s almost unsolvable, but also so simple, as anyone could start working toward a solution using just pencil and paper.

Last month, a cluster of computers spit out some intriguing possibilities. Sifting through the data, McLoud-Mann thought she found either impossible pentagrams (one’s that did not fit the problem), or ones that already fit into the 14 types that had been found.

But, this time it was different – the team came up with the first new convex pentagon able to tile the plane in some 30 years, joining only five mathematicians who have accomplished this feat. McLoud-Mann is considering what to do with the pattern – either tile a spot in her home or build a display of the pattern at her University of Washington site. To read the full original story, go HERE.

You know, I’m inspired to re-tile my bathroom with the new pentagon this weekend. I’ll let you know how it turns out.



“We’re Gonna Need A Bigger Boat”


Roger Kastel’s original JAWS artwork, three movie posters and a couple of the many JAWS parodies.

Click HERE to view the original video trailer.

We all know the spine tingling soundtrack – da, da, da, da, – da, da, da, da. Years later is still instills fear and anticipation.

Sharing our 40th anniversary here at KHT, and our love for cooling things and water (we look out over Lake Erie) Jaws is one of our favorite movies. And talk about a PIA (Pain in the @#$) Job – convince a group of beachgoers of the possibility of killer man-eating sharks in the water, and then set out on a small fishing boat to catch it, Jaws was unmatched in it’s action and suspense. Based on Peter Benchley’s novel of the same name, it starred Roy Scheider (as police chief Martin Brody), Richard Dreyfuss (as oceanographer Matt Hooperback and Robert Shaw (as the unflappable shark hunter Quint), all directed by the up and coming young Steven Spielberg.

Looking back today, the idea that there was once no such thing as a “summer movie season” seems inconceivable, as Jaws became the paradigm for the very idea of summer blockbuster films. Yet, this was the case in 1975 and the surprise success of Jaws chilled moviegoers to the bone, instilling a whole new fear of swimming and sharks.

So next time you go for a swim to “beat the heat”, think about your pals at Kowalski Heat Treating – and remember …. “da, da, da, da” …. You never know what’s lurking below.



Guess Dad Just Got “In the Mood”



40 years ago, Dad took a leap forward from his successful operations and management job and got “in the mood” to start his own business, centered on his strong family values, customer service approach and drive to deliver top quality work.  Today, following the same energy and initiative, we’re groovin’ – pushing things forward by continuing to invest in his vision, growing our service platform and inserting our energy into the business.

And the mood around here – simply fantastic!!

For our engineering friends, we thought we’d salute another 40th anniversary accomplishment, and a fellow “sensitive thermal processing” provider – The Mood Ring. Invented by two New Yorkers, Josh Reynolds and Maris Ambats, the mood ring became a fad in the mid 70’s, shared by friends and lovers to keep track of each others moods. Made from a specialized liquid crystal thermometer, the mood ring was wearable on the finger and usually ornamented with a faux gemstone made of quartz or glass and filled with thermo chromatic liquid crystal. Changes in temperature cause the crystal to reflect different wavelengths of light that in turn changed the color of the stone. Most mood rings were set up to display a neutral color at the average human skin temperature, approx. 37 degrees C. Each mood ring came with a color chart indicating the supposed mood the wearer was in – blue for calm, red for excited and yellow for nervous – perfect for young teens to watch and giggle about.

So next time you are stressed, or anxious about your PIA (pain in the @#$) jobs, slide on your old mood ring and give us a call – we’ll help you “chill out, baby” and “make sometin’ happen” on your next job. Peace, baby.



Shake It Up Baby


With the heat upon us, I couldn’t help but think back to my younger days and a Kowalski summer treat – creamy milkshakes. I always liked mine with a simple traditional hamburger and salty fries. My favorite memories were stopping on the way home from work at a small little ice cream shop and having a strawberry banana milk shake – real strawberries and very chunky!

Milkshakes began way back in the late 1800’s and actually started out as an eggnog type alcoholic drink. Many years later, the use of malted milk powder was popularized by Ivar “Pop” Coulson of the Walgreens drugstore chain, who made a milkshake by adding two scoops of vanilla ice cream to the standard malted milk drink recipe, making Walgreen’s in-store counter the place to be. Metal shake containers and high speed blenders made shakes a staple in the 50’s and 60’s. Since then, dozens and dozens of variations, and improvements, have been made, including adding fresh fruit to make popular “milkshake/ice” smoothies.

Like most things, ask around to find out who has “the best” milkshake, and you get many opinions. Along with the chain restaurants (e.g. Steak N Shake) my friends and staff have their favorite Cleveland locations – here’s my “Top 5” list to visit and some shakes to try:

  • Town Hall (W 25th) – traditional vanilla/chocolate shakes (try adult Nuts, Bourbon & Bacon)
  • Tommy’s (on Coventry) – milkshakes, malts and smoothies (try black raspberry chip)
  • B Spot (Cleveland, Columbus, Detroit, Indianapolis) – traditional and seasonal shakes (try chocolate banana marshmallow)
  • Mitchell’s Ice Cream (seven locations) – shakes, malts and smoothies (try strawberry with mango or cookies & cream)
  • Potbelly Sandwich Shop (on Euclid) – shakes, malts and smoothies (try Oreo or Coffee)

Stay cool!