Number Rules the Universe

“Geometry is knowledge of the eternally existent,” said the Greek sage.  So fundamental is this truth that every middle school includes geometry in its curricula.  

Coming of age, children, enter into the exquisite beauty of geometric truth.  Regardless of language spoken, color of your skin, which church, temple or forest you worship in, the eternal truths – πr² (area of a circle) or 2πr (circumference of a circle) or πr(r+l) = πr[r+√(h²+r²)] (total surface of a cone), et cetera – pertain.  Greek letters are used to label these eternal truths.  

At our Art Farm Homeschool Academy we study surface area in the conventional way, using worksheets and word problems.  But, on hands and knees, we examine the floor closely, teaching math as tactile, not just conceptual.  Last week we discussed electric currents and Ohms.  This week we turn to tiling, which is a form of applied geometry and chemistry, using hand tools to spread mortar and setting tiles to create one continuous surface.  

We began with Pythagorus.  To establish the layout, we needed to determine the exact right angle to the exterior wall, so the warhorse a² + b² = c² was used.  After marking the right angle, the center line was snapped and the layout became clear.  We used tiles 12” x 24” (2 square feet each) and my son quickly calculated the bathroom surface area was 136 square feet. 

Tiling is about surface, not volume; each tile must be flush at all four corners.  My son learned how to spread mortar, which again is about geometry.  A notched trowel is the tool, and depending on the size of the notch – 1/8” or 1/4” or 1/2” – the amount of mortar spread will vary greatly.  More importantly, the angle of the trowel impacts the thickness of the mortar, which is to say the volume.  The Professor used a sawtooth trowel and he taught that the proper angle was just below 45 degrees.  

To spread mortar is “to butter the tile.”  We “double buttered,” applying mortar both to the floor, as well as to the back of the tile, in order to create a stronger bond.  The tile is then set in place and gently pushed back and forth, to eliminate any gaps from the sawtooth troweled mortar, and to set the tile firmly and evenly in place.  

Tiling a bathroom floor is immensely disruptive.  We had to pull the toilet and bathtub, there was no laundry for more than a week, showers were intermittent.  When an object fell down the drain line we had to vacuum it out.  For anyone with obsessive tendencies, the process is like chasing, or being chased by, the dragon.  It was a long hard week.  

On the final day we set the grout, but the instructions wildly under stated the area covered by one bag.  Mid-way through we had to mix a second bag – which meant cleaning the tools and the bucket, getting fresh water, mixing more – but the working time was a factor for the grout already set.  If the grout cures before it is all set then you have a major problem.  We were racing the clock.  What we thought would be smooth teamwork became a gauntlet.  Like a farm boy, my son hustled, taking orders in real time. 

The marathon was grueling.  Our teamwork was successful, the timing worked out, the end result wonderful, the washer and dryer in place and operating again.  The radiant heat is working, programmed to 74 degrees at 5:30am, cooler to 62 during the day, and then reheat for the evening, back to 60 for the night hours. Verily, verily, I say unto thee, our blessings abound!

Through this gauntlet of fire my son is learning what the Greek sage said, so long ago, “Number rules the universe.”