THE MATH OF STYLE WRITING

We have so many style of fonts in any language. They are easily scalable. Their file size is very small in kilo bytes. How is it possible? Let us explore the interesting idea that create fonts.
We know how to plot a point in a graph and how to draw straight line. Two points are enough to make a st.line. Every line has a slope m. Slope is found by dividing the ,rise, of the line by 'run' of the line. The 'rise' is change in Y-coordinate between two points. The 'run'is change in X-coordinate.
Let the point be X1, Y1
Than the equation of a line is Y-Y1 =m(X-X1)

our case:
Slope of the line given in the figure is m = rise/run = 8 - 3/6-1 = 5/5=1
using slope and one point we can write the equation of a line

slope = m=1
point = (X1,Y1) = (6,8)
so Y-8 = 1(X-6)
Y-8 = X-6
Y=X-6+8
Y=X+2. This is the equation of the line. The short segment of line can be written as
Y=X+2, from X=1, to 6
Hence, to draw line, we do not need hundreds of points, just this one line is enough.

Now let us take the font of English letter 'V' and draw it on a graph sheet.
We get two inclined lines. Find their slopes and write their equations in point-slope form.
Line I:
slope m = 5-1/1-3
m = 4/-2= -2 (negative slope)
The equation of the line considering the point (1,5)
y-5 = -2(x-1)
y-5 = -2x+2
y = -2x+2+5
y=-2x+7
The equation of the line segment is y=-2x+7 from x=1 to 3

Similarly equation of the line II is
y=2x-5 from x=3 to 5

Just these 2 equations compactly represent the font 'V'. Suppose you double the coordinates of a point. The point (1,5) becomes (2,10). The font size increases Hence you can easily scale the fonts.
But the fonts are not made of straight lines but also by curves. But curves can be represented by polynomial equations.

Example: The equation 3x^2+2x+1 represents a parabola. 4x^3+3x^2 +2x+2 represents another curve. Using these kind of equations, we can construct fonts made of curves.
We can say, this is the simplest use of (analytical geometry).
Math is everywhere.
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