THE GOLDEN RATIO (φ)

Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Many artists and architects have proportioned their works to approximate the golden ratio as it is widely thought to be aesthetically pleasing.

The Greek letter Phi (φ) represents the GOLDEN RATIO and its value is: 1.6180339887 

The Golden ratio is the relationship between 2 numbers on the Fibonacci series where plotting the relationships on scale results in a spiral shape
The Golden ratio is everywhere:

Designer Cristian Ilies Vasile creates a work of art with the Progression and transition for the first 10,000 digits of φ

The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci around the year 1487 The drawing, which is in pen and ink on paper, depicts a nude male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man. 

In Michelangelo’s painting of “The Creation of Adam” on the ceiling of the Sistene Chapel, look at the section of the painting bounded by God and Adam.   The finger of God touches the finger of Adam precisely at the golden ratio point of the width and height of the area that contains them both.  

The Golden Section was used extensively by Leonardo Da Vinci.  Note how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion.

Information and Image source: Internet

The Science behind Cross-stitch embroidery

Cross-stitch is a type of counted thread embroidery in which X-shaped stitches are used in a pattern to form a picture.  It starts with a simple X shaped stitch that is commonly embroidered with floss on an even-weave Aida matte fabric.  The cross stitch is repeated numerous times to create a design.  Counted cross stitch designs are made by following a grid or chart where each square that contains a symbol represents 1 stitch.

A cross-stitch pattern is similar to a computer graphics image which is a rectangular grid of pixels of different colours. Simple mathematics is involved in the realm of counted cross stitch.

MEASUREMENT
First you start out by choosing your fabric. By using measurement you can determine the size that you need the design to be. Fabric count will determine the finished size of the design. The most common used fabric is Aida matte. Most designs give you different sizes for different counts of fabrics telling you the size of the finished design.

Secondly you need to find the center of the design and fabric. Next you need to find the center of your fabric, fold the fabric in half and then in half again, marking the middle square with a pencil/pen. This is where you will start stitching your design.

Cross stitching requires a lot of counting. One needs to determine the amount of floss that you will need for a section of the pattern. Estimate the amount of skeins for a color needed to complete the pattern. 

GEOMETRY

 Cross stitching incorporates angles, shapes, and coordinates. There are a lot of 90° angles, 45° angles, and 135° interwoven into a cross stitch pattern. Some patterns have symmetry.   

ALGEBRA

Algebra is used in cross stitching through ratios(rise over run), patterns, and meaningful use of reading symbols. By reading symbols you learn which color to use on the pattern.   

 

FRACTIONS

Cross stitching even incorporates fractions.  For the use of background filling, there are different types of stitches - half stitch, one-quarter stitch, and three-quarter stitch.

 - Half Stitch - The Half Stich is a diagonal stitch that goes from one corner of the fabric square to the opposite corner. Some designs use the half stitch to add interest and texture to backgrounds and shadows

 - Quarter Stitch – A quarter stitch resembles a half stitch but is half its length and only extends into the center of the stitching square.   Quarter stitches are often used to create details or to complete a three quarter stitch that has been stitched in a different color.

 - Three Quarter Stitch –Three Quarter stitches are used to create curved design lines.  This fractional stitch makes it possible to add detail to the otherwise “blocky” look of traditional cross stitch.

 - Quarter Stitch – Stitch 1-2 is the One-Quarter Stitch. When stitches 1-4 are worked in the same colour, the resulting stitch is called a Three-Quarter Stitch

Information and Image source: Internet

The Science of Tatting

Tatting is a handmade knotted lace formed with a fine thread and a tool called shuttle.

The shuttle works as a thread-holder and, as with a weaving shuttle, it moves between the threads on the loom of the hand - but that is the only similarity with weaving.

If you are looking at a pile of lace in a flea market, tatting will stand out from the rest because it is composed entirely of small rings, or rings and arched chains. These rings and chains are usually embellished with picots - tiny loops of thread between stitches. Some picots are purely decorative, but others are used for the vital function of joining elements together.

TATTING PATTERN

There are 2 types of tatting patterns that one can use to create a lace

1)     A written pattern has mathematical-looking notations and extensive use of abbreviations.

2)     In a visual pattern the design is drawn schematically with annotations indicating the number of double 

        stitches, picots, rings, chains and order of construction.

UNDERSTANDING A TATTED LACE

Various branches of the art of knotting make use of the Tatting knot.

If 2 half hitches are tied together on an idependent thread they form a double knot (as shown in fig1).

The thread on which the knots are tied is called the Foundation thread. If a number of these knots are made upon an independent Foundation thread, the result is a tatted chain(fig 2).

If one double knot is made at a slight distance from the one before it, leaving a ‘space’ of thread, when the knots are pushed up closely together this thread will remain as a loop between the two, this is the picot(as shown in fig 3).

When a sufficient number of knots have been made, the running line can be pulled tightly so that the last knot will be brought round to form a closed ring(as shown in fig 4).

DEVELOPMENT OF BASIC SHAPES

The ring itself is the most primitive basic shape. It can be used in various combinations to make simple geometrical forms.

A line of 3/more rings can be pulled round so that the last ring meets the first, forming an enclosed space between them. The piece can be any shape, according to the number of rings used. 

- 3 rings suggest a triangle with equal sides.

- 4 rings suggest a square.

- 5 rings suggest a circle or a pentagon

- 6 rings make a circle or a hexagon

- A larger number can be drawn into an oval

MAKING OF A TATTED FABRIC

To produce a piece of tatted fabric, any of the above motifs may be repeated and laid in rows, each joined to the next.

Triangles can be laid together in a number of ways

- 2 make a diamond shape

- 6 make a hexagon

- If another triangle is added to each of the 6 sides, the result is a 6-point star

- 3 six-ring circles can be combined to produce a triangular form and so on.

A 6 ring circle, which is in effect a hexagon, can be produced in all directions, every arm linking another to make a piece of fabric, rectangular or circular.

Any of the basic shapes can be added to by working other motifs around them, retaining or altering their original shape as needed.

Information and Image source: Internet