Additional Math Pages & Resources

Wednesday, January 6, 2010

Vertical and Horizontal

In the last few days I have talked about

1. Counting years, using charts with rows and columns of numbers.
2. Hanging mini-blinds and measuring carefully so they fit.

Today I see that several math concepts were used but not defined - vertical (columns) and horizontal (rows). We start teaching these concepts in kindergarten so kids become familiar with terms that define our relationship with objects around us.

When we draw, we assume the left side of the paper (or screen) to be vertical, and the sweep across from left to right to be horizontal (even if we are balancing a laptop on our knees or tilting our paper at an angle). When creating a math lesson I simply draw a box with Adobe Illustrator, and it is aligned so the vertical sides do go up and down.

Look at the following two shapes. We say that one has a horizontal orientation, and the other a vertical orientation - ABCD is horizontal, and WXYZ is vertical.

OK, so much for theory, in real life how do we determine horizontal or vertical ?

We say horizontal things are at right angles to vertical things.

That's not much help! you protest.

In "the real world" we find that there are very few objects or surfaces that are exactly vertical or horizontal. In fact, since the earth is (generally-speaking) round, what we take to be flat ground may be slightly curved. How can we measure this curvature? How do we determine vertical?
Horizontal surfaces are always at right angles to the gravity force exerted by a local astronomical body. Earth's gravity is pulling us downward; assuming we can measure in which direction that force is strongest, we can find vertical. A right angle to that is horizontal.

We have created ways to determine these directions - we can position a stick so it casts no shadow at noon, when the sun is directly overhead. We can drip water. We can use a plumb bob (weight on a string). Even a full glass of water will indicate horizontal and vertical. These tricks have been known for thousands of years.

Now we can use various kinds of bubble levels to closely adjust items to a vertical or horizontal position. Here's a fun animated level that you can buy if you have an HTC mobile phone.

And in today's ultra-high-tech hardware stores you can buy a laser level / plumb tool that helps you in this endeavor. These shoot red lines across the room or yard, enabling you to build things correctly.

Why would you care if things are level or vertical? You might not. Here's an argument against it,
 from Austrian artist/architect Friedensreich Hundertwasser:

The flat floor is an invention of the architects. 
It fits engines – not human beings.
We do not only have eyes to see and ears to hear and noses to smell.
We also have a sense for the touch of our hands and feet.

If man is forced to walk on flat floors 

as they were planned thoughtlessly in designers’ offices, 
estranged from man’s relationship and contact to earth
a decisive part of man withers and dies. 

This has catastrophic consequences for the soul, 
the equilibrium, the well-being and the health of man.
Man’s ability to experience ceases and he becomes disabled,
mentally and organically.

An uneven and animated floor 

is a means to recover dignity of man 
which has been violated 
in our unnatural and hostile urban grid system.

The uneven floor becomes a symphony, a melody for the feet.

It brings back natural vibrations to man.
Architecture should elevate and not subdue man. 

It is good to walk on uneven floors and regain our human balance.

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