Tutorials

How to Draw the Letter O
to any size without measure

You can draw the letter O without measure using the square, the circle, and their derivatives. It can be scaled to the size of a cathedral, or a crop circle, or even the size of The Great Pyramid of Giza. The larger the square the more accurate the drawing will be.

Draw a perfect square.

Divide the square into quarters.

THE EIGHT POINTED STAR

Draw a total of eight lines: two lines from the centers of each side of a square to its opposing corners.

Label the intersections.

Draw a 1, 2, √5 triangle by connecting points LCI.

Next, draw 1, 2, √5 Triangle KAD.

The overlapping 1, 2, √5 Triangles create rectangle 1234. This rectangle is a triple square.

From center point A open compass to point B which is tangent to the center octagon, shown as a dashed line, that was formed from the Eight Pointed Star. Inscribe a circle.

At the intersection of the Circle and the Triple Square inscribe rectangle 5678. This rectangle is a Double Square.

Draw 1, 2, √5 Triangle 567 by drawing diagonal line 57 across the Double Square.

Place compass on point 7. Open to point I and inscribe a circle.

Place compass on point 5. Open to point A and inscribe a circle.

Draw line ab through the intersections of the overlapping circles. Line ab creates the axis upon which the counter of the letter O is built.

Line ab intersects the double square 5678 at cd. This creates two additional 1, 2, √5 triangles within the double square.

Place compass point on d and open to the smaller inner circle at e.
Inscribe a circle.

Place compass point on c and open to the smaller inner circle at g.
Inscribe a circle.

Place compass point on center of foursquare z and open to perimeter of four square at E.
Inscribe a circle.

A beautiful arrangement of center points formed from 1, 2, √5 triangles foster five circles. These five circles fully describe . . .

. . . the Roman Letter O.

The center points, generating the letter, serve as a sort of atomic big bang or sephiroth in the creation of the Roman letter O.

We have constructed the letter O using the 1, 2, √5 triangle and the Eight Pointed Star. To confirm the letters geometric efficacy we find the letter can also be described using the 3, 4, 5 triangle. The absolute beauty of these two different triangles both answering the constructive structure of the letter is outstanding. The letter O is geometrically perfect.

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Meditation

How to Draw the Letter K
to any size without measure

The developmental drawings of the letter K will reveal to us its intricate structure based on the Eight Pointed Star. We are doing this without the need to measure. I have included a ghosted image of the K in each drawing so that you can see how the geometry progresses to its goal. The Eight Pointed Star is a simple form yet the use of it in creating every nuance of the Roman alphabet is creative and complex.

Draw a perfect square.

Divide the square into quarters.

THE EIGHT POINTED STAR
Draw a total of eight lines: two lines from the centers of each side of a square to its opposing corners.

Draw four EIGHT POINTED STARS within the larger Star.

Locate center points for the four serifs of the K’s down stroke based on the grid.

Note that the dashed lines are drawn through various intersections of the grid (as shown by the arrows) to help identify the center points.

Find the center point for the lower outer curve of the K. The center point may be found by employing the 1, 2, √5 Triangle. Note that you do not need to measure the triangle. Following the grid as shown will establish its precise proportions.

Establish the center point for the outer curve of the upper serif employing the 1, 2, √5 Triangle, and again, as always, without the need to measure.

The bold dashed line (going through intersections of the grid) establishes a shared apex of two 1, 2, √5 Triangles. Draw the circle for the small inner curve of the upper serif at the intersection of the centerline of these triangles and the grid.

This becomes very interesting. The bold dashes identify a 3, 4, 5 Triangle. It’s Unit 5 hypotenuse establishes the Unit 1 base of a 1, 2, √5 Triangle. The unit 2 leg of this triangle is the outer leg of the letter K. This is a good example of how the triangles play creatively amongst the grid.

The bold dashes identify another 3, 4, 5 Triangle. Where it’s Unit 5 hypotenuse crosses the hypotenuse of a previously established 3, 4, 5 Triangle, a center point to the small inner curve of the K’s lower leg can be found.

The seemingly innocent little circle that we just previously drew, intersects with the hypotenuse of the 3, 4, 5 Triangle and establishes the corner of a 1, 2, √5 Triangle. This identifies a point for the inner leg of the letter K! Please note how the vertices of the bold triangle kisses the perimeter of the square.

Look at this bold triangle! Do you see how two previously established center points extends a line outwards to create the Unit 1 leg of the 1, 2, √5 Triangle, giving us the upper outer leg? Again, look at how the 3 vertices play with the puzzle.

CRAZY PRECISION.

Oh K!

We have constructed the letter K using the 1, 2, √5 triangle and the Eight Pointed Star. To confirm the letters geometric efficacy we find the letter can also be described using the 3, 4, 5 triangle.

The absolute beauty of these two different triangles both answering the constructive structure of the letter is outstanding. The letter K is geometrically perfect.

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Tutorials

How to Draw the Letter O
to any size without measure

How to Draw the Letter K
to any size without measure

What to Read Next

Arche-Type Geometry

Site Map

Tutorials

How to Draw the Letter O to any size without measure

How to Draw the Letter K to any size without measure

What to Read Next

Arche-Type Geometry

Site Map

How to Draw the Letter O
to any size without measure

How to Draw the Letter K
to any size without measure