Circles In A Spiral

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About Richard Murison

Round Like a circle in a spiral Like a wheel within a wheel Never ending or beginning On an ever spinning reel Like a snowball down a mountain Or a carnival balloon Like a carousel that's turning Running rings around the moon Like a clock whose hands are sweeping Past the minutes of it's face And the world is like an apple Whirling silently in space Like the circles that you find In the windmills of your mind!

Like a tunnel that you follow To a tunnel of it's own Down a hollow to a cavern Where the sun has never shone, Like a door that keeps revolving In a half forgotten dream, Or the ripples from a pebble Someone tosses in a stream Like a clock whose hands are sweeping Keys that jingle in your pocket Words that jangle in your head Why did summer go so quickly? Was it something that you said? Lovers walk along a shore And leave their footprints in the sand Is the sound of distant drumming Just the fingers of your hand?

Pictures hanging in a hallway And the fragment of this song Half remembered names and faces But to whom do they belong?

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He: when you knew That it was over You were suddenly aware That the autumn leaves were turning To the color Of her hair! She: when you knew That it was over In the autumn of goodbyes For a moment You could not recall the color Of his eyes! Main menu Search. Hide Menu. Rollin' Rollin' Rollin' Two circles of equal radius touch at P. How Far Does it Move? Like a Circle in a Spiral. One of my regular trips to Liverpool last summer took me to the Walker Art Gallery. A wonderful place with some beautiful pictures.

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On my way out I stopped to browse in the small shop and discovered this toy for 50p. So here are some things for you to think about. It is important to remember that it is the argument you use to justify your decisions that is most important. We'll therefore start by constructing a golden rectangle I'll explain what it is when that's done. Construct a square. Forgotten how? See Working With 4 and 8. An A4 piece of paper or any other size in the A series is a golden rectangle, so you could use its total surface as the outer rectangle, and go straight to step 6.

We now need to break this rectangle down into squares. We already have the first square. The next one will be taken out of the rectangle BGHC. Repeat this operation in each successive rectangle, always creating the square against the outer edge of the rectangle.

When we have enough squares, or they become too small to work with, we can draw the spiral proper. Place the dry point on C, let the opening be equal to the side of the first square, and draw a quarter of a circle DB. Move the dry point to I, reduce the opening to the side of the second square, and draw an arc BJ. The feel of this spiral is very different from the concentric and even static appearance of the regular spirals: it's much less contained, with dynamic movement.

Circles can be inscribed, i. This device is the basis for much of the decorative geometry of the West, for instance in Celtic illumination or Gothic rose windows. We'll look at two basic constructions that we can use with any polygon or any number of circles inside a circle, and then construct two full-fledged windows with their tracery. This method allows you to fit the number of circles of your choice inside a circle. Start by dividing your circle evenly in the desired number of sections, then for each sector proceed as follows. The sector shown here is from a circle divided in six.

We now need to draw the perpendicular to PQ in Q.

With the dry point of the compass on Q, and any opening, draw an arc that cuts the bisector at point A. Point O is the centre of the circle inscribed in this sector. The circle can now be drawn, with the compass point on O and the opening set to OQ. Here are some possibilities, depending on the number of sectors the circle was divided into.

Rick Mohr - Spiral of Circles

Note that, the circles being tangent, the arcs between their contact points can be omitted to create rosettes. This method is to fit a number of circles in a polygon equal to the number of sides of that polygon three circles in a triangle, five in a pentagon, four or eight in an octagon First connect the centre of each side to the centre of the polygon, thus dividing the polygon into kites, and then proceed as follows for each kite.

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O is the centre of our inscribed circle, but in order to determine the radius of the circle accurately, we need to find a point F on AD so that OF is perpendicular to AD. This is the purpose of the remaining steps:. As with the previous construction, different polygons will result in different shapes, and the the inner arcs can be erased to create rosettes.

Such church windows betraying a Celtic influence can be spotted in many places around the British Isles. To draw the tracery of the window, i.

Place the dry point where one of the intersection of a diameter with the last circle we drew, and set the opening to the difference between the two large circles. Draw a small circle. Return the dry point to the original centre and open it as shown. Draw a third, innermost large circle. Start with a large circle. Divide it in eight, by following the steps for drawing a square there's no need to draw the square itself, because we only need its diagonals.

Square Circle Spiral

The sides of the octagon cut the diameters at eight points. Join these to create an inscribed, dynamic octagon.


Now, returning to the numbered points, join the following pairs: and , then and Notice the following places where three lines intersect: they are the centres of the eight circles forming the rosette. Change the opening of the compass as shown here, and repeat. There is no need to draw the full circles—you can stop the arcs where they meet a diameter, and ink them that way. With this chapter on circles, we have completed the basic part of these lessons on geometric designs. From next month on we will focus on complete patterns and motifs of increasing complexity, from both East and West. Unlimited asset downloads!

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This post is part of a series called Geometric Design for Beginners. Geometric Design: Working With 5 and Geometric Design: Knots and Weaves. What You'll Be Creating We have already used circles extensively to create various grids for a number of patterns. Spirals Spirals come in several different types.

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