How to draw a trefoil within a circle School Curriculum: Key Stage 4 mathematics: The trefoil within a circle extends the work on trefoils. In a trefoil a circle circumscribes the three vertices of a triangle. This enables the placement of the three foils or arcs centred on each of the verteces of the triangle. Here the exercise is repeated but with the addition of a circumcircle, still centred on the circumcentre, i.e. the centre of the triangle, but at a tangent to each of the three foils. Extra decorative arcs embellish the work. The trefoil was brought to England by French masons in the first half of the thirteenth century. Binham Priory in Norfolk, now a romantic ruin, then a thriving Beneditine monastery, vies with Westminster Abbey as the location in which it first appeared.

School Curriculum: Key Stage 3 & 4 Mathematics: drawing angles using a pair of compasses and a straight edge; centroid of a triangle; congruent circles within a circle: manipulating shapes, Pythagoras Theorem and the sine rule; Properties of 30°-60° 90° triangle: Drawing a mouchette is based on circle stacking, i.e. arranging three congruent circles within a circle. The window at St Thomas of Canterbury, Northaw required builders to find appropriate centres of the smaller congruent cirlces when the larger circle had been designated. To effect this the design could often be manipulated mathematically to produce a triangle that in turn enabled calculation of sides or angles by the 30° -60° -90° rule if a right angle was present. It was a short step from the reticulated Curvilinear tracery (see relevant lesson plan) to the use of a mouchette as a motif. A mouchette is a daggerlike motif found most often in 14th century Decorated church tracery. It is formed by elliptical and ogee curves that produce a point at one end and an incomplete circle at the other.

How to draw a single Anglo-Saxon church window or door opening The Anglo-Saxon tower at the Church of St Peter, Barton-Upon-Humber, Lincolnshire was built in the late tenth century . The double triangular opening is divided by a bedimmed single shaft. The triangular form is constructed by leaning two stones together at an angle. The blind arcading and vertical pilaster strips of stone emulate beams used in the construction of timber-framed houses. School Curriculum: Key Stage 2 Mathematics: For younger students of the Key Stage, drawing the doors and windows extends understanding of how simple shapes can be combined, manipulated and applied outside the classroom. The drawings require measuring angles with a protractor and the exercise can be extended to calculate the area of a rectangle and a triangle.

How to draw a large Geometric window in the Decorated style School curriculum: Key Stage 4 Mathematics: Drawing the Altrincham window would support the teaching of the 2D stacking of circles. It is concerned with the optimal arrangement of placing four congruent circles within a circle, and related problem solving using Pythagoras. Altrincham Baptist Church, Cheshire was constructed towards the end of the Gothic Revival movement in 1904; its west window is shown on the accompanying pages. The window comprises five lancet lights. From the left, there are two lights under a circle within a sub-arcuation; then a single light under a circle circumscribing four congruent circles; then two lights under a circle within a sub-arcuation; all within a larger arch.

This lesson develops the theme of the ogee or s-shaped arch (see relevant lesson plan). In the church window at Finedon, the apex comprises a vesica atop two vesicas that are curved at top and bottom into ogees, all in a net-like arrangement. The apex is set above three lights with ogee arches. This type of tracery is termed reticulated Curvilinear. School Curriculum: This is the first of four studies of different types of Decorative window. Each has a design that is an arrangement of circles or arcs with the same radii, within a defined perimeter, with or without overlaps. An analysis of the windows at Finedon reveals that the architect simply stacked a series of congruent windows and equilateral triangles. The windows studied are within: the Church of St Mary the Virgin in Finedon: the only window with overlaps; St Thomas of Canterbury, Northaw (available on another page); Altrincham Baptist Church (ditto); and Lincoln Cathedral (ditto). This series of lessons is well suited to project work at IB / GCSE level. However it arose, the ogee arch rapidly led to the development of many different tracery designs. Whereas earlier windows had a static non-directional element, now the ogee enable both mullions and tracery to intersect, curve and flow from one shape to another with an arabesque character that became known as Curvilinear tracery.

The Angel Choir window in Lincoln Cathedral Once a single or pair of lights surmounted by a quatrefoil within a circle had been constructed (see relevant lesson plans), masons were quick to realise its potential for larger areas, by increasing the number of lights and circles. Large C13th windows of the Geometric period had an even number of lights arranged in pairs, each pair with its own circle. The largest example is the eight-light Angel Choir window in Lincoln Cathedral where the window is made up of eight lights, arranged singly, yet in pairs, and also in fours, i.e. two times two pairs, or four + four lights, with a total of thirteen circles of different sizes in the window apex. School Curriculum: Key Stage 4 Mathematics: The Sine Rule. In a similar way to the apex window at Altrincham Baptist Church, and the mouchette wheel at St Thomas of Canterbury, Northaw, (see relevant lesson plans) the circular window in the apex of the Angel Choir window at Lincoln Cathedral required builders to find appropriate centres of the inscribed congruent, circular windows, or circles. In the Angel Choir window, there are six circles, each tangental to the circumscribing circle, and to two neighbouring inscribed circles. There is also one inner circle; with the inner circle being inscribed by the six inscribed outer circles. Applying the sine rule provides a formula for finding the radius (rs) of any number of inscribed circles where (rl) = radius of the circumscribing circle, and angle x are known. Photo credit: Jules & Jenny

How to draw lancet triplets Once the students are at ease with drawing a lancet window (see relevant lesson plan) then try lancet triplets using the illustrated ieasy-to-follow instructions. A very elegant window arrangement is to draw the triplets together with the centre light being taller and slightly wider than the outer lights. A good example can be seen at Temple Church in London, completed in 1240. Each light has its own dripstone. Within the dripstone are mouldings that descend onto the capitals. The capitals sever the multiplicity of mouldings from the single shaft below thereby producing a pleasing contrast.

How to draw a lancet window with trefoiled apex The instructions for the drawing on the following pages are based of a window in the nave at St Botolph’s Church in Northfleet Kent. The dimensions produce a drawing of a window that fits on an A4 page. Precision is required, and the task is easier on an A3 page, in which case the dimensions should be doubled. Botolph was a saint venerated in the seventh century in the Kingdom of East Anglia, where he had lived as a monk in an abbey endowed by estates in the Kingdom of Mercia. Botolph mediated a fragile peace between these two warring states. After his death, Botolph’s relics were conveyed to many different places where churches were later dedicated to St Botolph. As these churches were erected next to the cities’ gates or by fords, bridges and shire boundaries, he has become associated with travellers.

In Asia Minor the horseshoe arch has long been a structural and decorative motif adorning tombs, sarcophagi and stele. After the Eastern Christian Church adopted the shape it quickly spread to North Africa, Spain, Gaul, Italy and Rome itself. How to draw a horseshoe arch: School curriculum: Key Stage 4: measurement of arc length Maths covered: Arc length is the distance between two points on a curve. and is usually denoted by l or s, the latter from the Latin spatium meaning length or size. s = (θ° ÷ 360°) x 2 π r where theta θ is a measure of the angle subtended by either ci-e-di & co-e-do (fig. on lesson plan in degrees, π = 3.14 and r = the distance ae (fig.) in centimetres If the arc is a semicircle then s = π r This lesson would serve as an extension of the lesson on a Roman arch and brace, itself extended by the lesson on a Romanesque or Norman arch

This exercise builds on earlier lessons on Gothic Early English architecture. It is a complex drawing suitable for top set project work for GCSE students Content: the first exercise is a simple construction of a quatrefoil. It is followed by detailed and illustrated instructions on how to draw two adjoining trefoiled lights under a arched dripstone. The instructions that follow fills the apex above the two lights with a quatrefoil, with an option to do so with a pointed quatrefoil.

Key Stage 2 & 3 mathematics: Rotational symmetry occurs when a shape, on being rotated around a centre point a number of degrees, appears the same. The order of symmetry is the number of positions that a shape appears the same in a 360-degree rotation. An equilateral triangle has rotational symmetry of order three, i.e. it may be turned about its centre point into three identical positions. A trefoil and a pointed trefoil (see appropriate lesson plan), being constructed on an equilateral triangle, may be turned about their centre points into three identical positions, i.e. both have rotational symmetry of order three. Key Stage 4 mathematics: A circle which touches the three vertices of a triangle is called the circumcircle of a triangle. The centre of a circumcircle is the point where all the perpendicular bisectors of the triangle’s sides meet. This point is called the circumcentre. The radius of the circumcircle is termed the triangle’s circumradius. Having drawn a regular polygon, arcs can be drawn with their centre points at the vertices of the polygon, and the radii equal to half the length of the edges of the polygon. In this way a trefoil, quatrefoil, cinquefoil or multifoil is formed when each arc just touches its neighbours. In 1254 a Catholic religious order was founded in France called the Order of Saint Augustine. Monks of this Order followed the teachings of St Augustine of Hippo who, in the fifth century, advocated the virtues of chastity, poverty and obedience as essential for a religious life. The monks were obliged to live together in peace and harmony, to share labour, pray together, and eat in silence. They were also to look after the sick. Pilgrims flocked to their monasteries one of which was the Sanctuary of Rocamadour in South-West France. It is a spectacular monastery built into the side of a cliff on the pilgrim route known as the Way of St James. Unusually it has made use of lancet and trefoil design for an entrance.

How to draw an ogee arch Illustrated and easy-to-follow instructions on how to draw an ogee arch. The ogee or S-shaped arch is the principal architectural feature of the Decorated period church window. The ogee as an architectural motif has a long history: it had been used in India in antiquity; it arrived in Egypt in the ninth century, then in Venice in the thirteenth. Soon after it appearance in Venice, it turned up in England. Theories explaining the ogee’s appearance in England are explored. School Curriculum: Key Stage 3 Mathematics: Draw and manipulate triangles, arcs and semicircles with increasing accuracy; identify their properties, including line symmetry.