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Listen, Mate, My Friend Is Pythagoras

I am a school teacher with a love for writing short stories, usually with a humorous twist.

When I began University, my parents supported me financially as best they could and I supplemented my meagre income with whatever part time employment came my way. During one Christmas vacation, this included servitude as a builder’s labourer with the Chain Gang, a small construction company.

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My job description stipulated that I be indentured to the Chain Gang’s tight-knit larrikins consisting of carpenters (‘chippies’), electricians (‘sparkies’), bricklayers (‘brickies’), plumbers (‘dunny divers’) and a number of other tradesmen.

I thought I was up to par with Australian colloquialism and I knew that ‘dunny’ is slang for toilet, but I ventured, on my first day at work after perfunctory introductions were made, to ask Paul, the plumber, why members of his profession are referred to by the moniker, ‘dunny divers’.

“Ask me again after you’ve plunged your hands into a blocked, unflushed toilet just as the pipe erupts and spews its aromatic contents all over you,” he laughed sardonically.

Paul’s remark was prophetic; a week later, in his capacity as my supervisor, he ostensibly guided me as I dug into wet and malodorous soil to locate a blocked sewer.

However, ‘supervisor’ was a euphemism. Paul’s sole contribution to my edification as an apprentice ‘dunny diver’ was to cast gratuitous gestures of paternalism, including, ‘sewer vapours are good for your skin’ and ‘this sure beats going to University, doesn’t it?’

I laughed each time and thanked him for his advice.

It was not long before my inexperience and subservience became a segue for the Chain Gang to try to amuse themselves at my expense. As a neophyte in a tradie’s environment, I was in the firing line for traditional teasers.

One day, Dan, the chippie, instructed matter-of-factly, “George, you need to go to the hardware store and get me a left-handed screwdriver.”

I was not completely naïve, but I played Dan’s game.

“Okay. But I better ring first to see if they have any in stock,” I stated, taking out my phone.

Dan appeared puzzled at this response, but he welcomed the opportunity to witness my alleged conversation with the hardware store. He was already mustering other tradies and filling them in. I moved far enough away, pretended I was in conversation and returned to the group.

I looked directly at Dan. “The store says a new shipment of left-handed screwdrivers has just arrived, but he asked whether you want a Flathead or a Phillips?”

Raucous laughter ensued, and Dan appeared especially sheepish. The Chain Gang were uncertain as to whether I had really called the store. A further test was brewing. It was Mario, the big, jovial painter, who up the ante.

He ribbed me with, “Hey George, can you get us a gallon of striped paint?”

I immediately countered with, “Yep. But if they don’t stock striped, will polka dots do?”

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More boisterous laughter. Each tradie slapped me on the back as they walked off to resume their work. My rite of passage was complete.

In the following weeks I would mumble under my breath, “It’s good, honest work” each time I pushed a wheelbarrow laden with fresh concrete mix through a war zone of machinery, mounds of spilt dry concrete and wood cast-offs. It was hard to maintain stability. The swirling concrete effected changes in the barrow’s centre of mass, so that several times I lost control and fell in a most undignified way, doused with a heavy concrete brew. The Chain Gang would laugh, but there was also a burgeoning admiration when they saw that I was ‘having a go.”

I reciprocated the admiration when I came to appreciate that a tradie’s work represents the epitome of mathematics in action.

One crisp morning, I watched as Dan began constructing a timber frame to be used as an outdoor shed.

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To determine if the beam and the post are square (at right angles to each other), he measured 30 cm and 40 cm from the corner and checked to see if the length of the brace was 50 cm. When I asked Dan why this works his cryptic reply was, “Listen, mate, my friend is Pythagoras.”

He went on to explain that there is a famous mathematics formula known as the Theorem of Pythagoras that connects the side lengths a, b, c, (with c the longest side) of a right-angled triangle by the formula a2 + b2 = c2.

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My mind drifted to thoughts of a claustrophobic classroom a decade ago when a stuffy mathematics teacher tried to explain to us the theorem using areas of squares on the sides of a triangle. I never did grasp it properly. After all, I’m a mere Arts student.

“This means that any combination of numbers that satisfies the formula is proof that the triangle is right-angled,” Dan stated, dragging me back to the present.

“One combination that works is a = 3, b = 4, c = 5, because 32 + 42 = 52 or 9 + 16 = 25. That’s why we call it the 3 – 4 – 5 method.”

“But you didn’t use 3, 4, 5,” I challenged, somewhat cocky.

“Any multiple will work,” he replied with erudition. “The lengths are also independent of units. I used 3 x 10 = 30 cm, 4 x 10 = 40 cm, 5 x 10 = 50 cm, but I could have used 3 x 6 = 18 feet, 4 x 6 = 24 feet and 5 x 6 = 30 feet, or any other convenient Pythagorean triple generated from 3 – 4 – 5 .”

My next encounter with Pythagoras took place several days later. Gino was the Chain Gang’s concreter but also the artist in residence. Weeks ago I assisted as he expertly laid slab after slab to cover a large area in front of a house under construction. Now it was time to overlay the rough concrete with an intricate design using coloured grout.

“Fetch me the rope, mate,” he said, pointing to a bundle of gear.

I returned with a coiled length of rope and handed it to him.

“What’s this for?” I asked.

“Listen, mate, my friend is Pythagoras,” Gino replied, echoing Don’s guiding principle.

He uncoiled the rope and stretched it flat on the concrete. The rope was 3 metres in length and graduated with hollow markers 25 centimetres apart.

Gino inserted a masonry nail through the first and last marker and secured it to the concrete. He nailed the sixth marker, instructed me to pull back on the rope until a taut triangle shape was formed and nailed this point down.

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“Is this a 3 – 4 – 5 triangle?” I ventured to ask.

“You betcha,” Gino replied. He took an aerosol can of spray paint and traced a neat line along each side, using the rope as a guide.

“Now let’s get cracking,” he explained. As Gino finished each triangle, I sprayed the lines. It took several days for us to complete the concrete mural.

“Bellissimo, bonzer,” Gino commented in Italian and Australian slang. I’m sure Pythagoras would have agreed.

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The brickie of the group was ‘Lightning Reg’; slim, tanned and muscular. I observed him lay a course (a row of bricks) with incredible speed and unerring accuracy. There was no need for him to use a laser, level or plumb line to check the vertical integrity of a wall. Years of experience provided him with a sixth sense for such things, but I was to find out that he liked the traditional approach to see if a wall is horizontal.

The first few courses need not be completely level because they are below ground level and not visible, but subsequent layers must be horizontal.

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Reg disposed of the first two courses in record time and encouraged me to complete the third, scrutinising my efforts all the while. What appeared child’s play in his hands vexed me considerably, even when I tried to follow his advice.

Reg was encouraging at the beginning with gems such as, ‘more mortar on your trowel’, ‘tap gently to align the brick’ and ‘rough side up’. Soon, exasperation at my ineptitude took over, and I heard him say playfully, ‘Haven’t you ever played with Lego Bricks?’, followed shortly thereafter with a karaoke rendition of ‘Joshua fought the battle of Jericho and the walls came a-tumbling down.’

After my lacklustre efforts, Reg hammered into the ground a pole at each end of the unfinished wall.

“Bring the 20 metre tubing,” he directed. On the ground lay several rolled up balls of clear plastic tubing, about one centimetre in diameter. I grabbed the one with 20 m written at its end. Reg walked to the first post, grabbed one end of the tube and began unwinding.

“Grab the other end and hold it near the top of the other pole,” he called out.

I did so, and then watched as he inserted the syringe end of a plastic bottle into the tube and squeeze, forcing coloured liquid to flow like a transfusion.

“Do you know what I’m doing?” Reg asked, expecting a considered response.

I was still baffled, but I camouflaged my ignorance with a confident answer.

“You want to see how the liquid changes colour with pressure changes in the hose.”

“You berk,” Reg retorted in a friendly way.

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“The water levels at the two ends of the hose lie in a horizontal plane,” he explained.

“And that’s the line of reference we will use for each course of bricks.”

Without further comment, we marked the water level on each post, connected the marks with builder’s string and resumed the bricklaying.

“At least there’s no Pythagoras,” I observed wryly as I passed bricks to him.

“Listen, mate, my friend is Pythagoras,” he gestured, pointing a finger at me and tossing me a hypothetical.

“If the poles represent stumps of a house, you’d want to be sure they are square and of the same height. So you fix the height using the water hose method and check for squareness using Pythagoras’ formula.”

“Ah, I never thought about it that way,” I confessed.

We continued working for some time. Reg stopped and looked directly at me.

“By the way, did I tell you why Fibonnaci is also my friend?”

He smiled and winked. It was a story I was looking forward to hearing.