Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps. Some tiling puzzles ask you to dissect a given shape first and rearrange the pieces into another shape. Other tiling puzzles ask you to dissect a given shape while fulfilling certain conditions; the two latter types of tiling puzzles are called dissection puzzles. Tiling puzzles may be made from wood, cardboard, plastic or any other sheet-material. Many tiling puzzles are now available as computer games. Tiling puzzles have a long history; some of the oldest and most famous are the Tangram puzzle. Other examples of tiling puzzles include: Conway puzzle Domino tiling, of which the mutilated chessboard problem is one example Eternity puzzle Geometric magic square Puzz-3D Squaring the square Tantrix T puzzle PentominoesMany three-dimensional mechanical puzzles can be regarded as three-dimensional tiling puzzles. Dissection puzzle Polyforms Sliding puzzle Tessellation Wang tile
Reinhold Tiling was a German engineer, pilot and a rocket pioneer. Tiling was born as the son of a pastor. Shortly after he began the study of mechanical engineering and electro-technology he found himself in war service at the beginning of the First World War. In 1915 he volunteered as a fighter pilot in the newly created German Luftstreitkräfte. In 1926 Tiling became flight controller of Osnabrück airport, he began to explore rocket technology during this period inspired by Hermann Oberth's book "Die Rakete zu den Planetenräumen". Tiling developed re-usable rocket planes which start as a land with swinging-out wings; this principle was used by NASA for flights of the Space Shuttle. His innovation allowed him to develop rockets which had the necessary thrust and burning duration for flight. In 1929 Gisbert Freiherr von Ledebur allowed Tiling the use of a workshop in Ahrenshorst. In June 1929 some successful demonstrations were completed during which missiles reached a height of 1,000 metres. On 13 March 1931 Tiling and his co-worker Karl Poggensee succeeded in the launch of a solid-propellant rocket.
The rocket reached a height of 1,800 metres. Further rocket launches were undertaken in the following weeks; the break-through experiment occurred on 15 April 1931, when Tiling demonstrated a post office rocket which carried 188 postcards reliably. Further tests showed the reliability of his rockets; the rockets attracted large public interest. This attracted the attention of the Reichsmarine, developing rockets for military use since 1929. Despite the support of friends and sponsors, Tiling's work was beset by financial difficulties. On 10 October 1933, the overheating of the powder needed to power the rocket created an explosion in Tiling's workshop in Ahrenshorst, they succumbed to these injuries on the following day with Tiling dying in Osnabrück. A crater on the backside of the moon is named after Reinhold Tiling, located at coordinates 53° 06' S 132° 36' W. Rocket mail9783862251063 ISBN Reinhold Tiling: ǂb Flieger und Forscher, Erfinder der Kammerrakete / ǂc Klaus Tiling, Martin Frauenheim.
Reinhold Tiling – Pionier der Raketentechnik
In agriculture, tile drainage is a type of drainage system that removes excess water from soil below its surface. Whereas irrigation is the practice of providing additional water to soil when it is too dry, drainage reduces the moisture in soil and thereby increases the amount of air in its pores so as to augment conditions for optimal growth of crops. While surface water can be drained by pumping, open ditches, or both, tile drainage is the most prudent practice for draining subsurface water; the phrase "tile drainage" derives from its original composition from tiles of fired clay, i. e. ceramic, which were similar to terracotta pipes yet not always shaped as are pipes. In the 19th century a "C" shaped channel tile was placed like an arch atop a flat tile, denominated the "mug" and "sole", respectively. Today, tile drainage is any variation of this original system that functions in the same mode. HDPE and PVC tubing denominated "tile line" is used, although precast concrete and ceramic tiles are still used.
Excess subsurface water is counterproductive to agriculture because it fills the pores of the soil and evacuates the air they contain. Roots of plants require a quantum of air to live and grow, therefore excess subsurface water inhibits their growth and, if deprives them of air for a sufficient duration, causes their rot and death; such detriments to the roots of crops kills growth of the crops above ground. Additionally if detriment to roots of crops is excluded, another crucial reason for drainage is that an excess of water can limit access to the land by heavy machinery: vehicles and trailers sink in and rip up wet soil and may become stuck in it. Access to a field is crucial because most modern agriculture depends on use of heavy machinery to cultivate the seedbed. Most crops require specific soil moisture conditions, do not grow well in wet, mucky soil. In soil, not mucky the roots of most plants do not grow much deeper than the water table. Early in the growing season when water is in ample supply, plants are small and do not require as much water.
During this time, the plants do not need to develop their roots to reach the water. As the plants grow and use more water water becomes more scarce. During this time, the water table begins to fall. Plants need to develop roots to reach the water. During periods of dryness the water table can fall faster than the rate at which plants grow roots to reach it, which condition can gravely stress the plants. By installing tile drainage, the water table is lowered and plants can properly develop their roots; the lack of water saturation of soil permits oxygen to remain in the pores of the soil for use by roots. Drain tile prevents the roots from being under the water table during wet periods, which can stress the plants. By removing excess water crops use the water. An increase in crop yield can be summarized as forcing plants to develop more roots so that they can absorb more nutrients and water; the same principle operates in the pots of house plants: their drainage holes in the bottoms evacuate excess water from the medium so that air can fill the pores of the medium and be available to the roots which, if deprived of air by the saturation of the medium with water for a sufficient duration, will rot and die.
Installing tile drainage in a field in a grid pattern achieves the same effect for a field of several hundred acres. In a tile drainage system, a sort of "plumbing" is installed below the surface of agricultural fields consisting of a network of below-ground pipes that allow subsurface water to move out from between soil particles and into the tile line. Water flowing through tile lines is ultimately deposited into surface water points—lakes and rivers—located at a lower elevation than the source. Water enters the tile line either via the gaps between tile sections, in the case of older tile designs, or through small perforations in modern plastic tile; the installation of the tiles or tile line can involve a trencher, a mole plough, a backhoe, or other heavy equipment. Soil type affects the efficacy of tile systems, dictates the extent to which the area must be tiled to ensure sufficient drainage. Sandier soils will need little, if any, additional drainage, whereas soils with high clay contents will hold their water tighter, requiring tile lines to be placed closer together.
Tree roots of hedgerow and windbreak trees are attracted to the favorable watering conditions that adjacent fields' tiles or tile lines provide. Hydrotropism plays a role as root hairs at the dynamically probing tips of tree roots respond differentially to moister crevices versus drier ones, exchanging hormonal messages with the rest of the tree that encourage them to concentrate on advancing into such favorable niches. In the perforations of tile drainage lines, just as in cracked or rusting water lines and sewer lines under town streets, these roots find the ideal combination of an entrance to enter and a plentiful water supply behind it; the result is that in any of these pipe systems, blockages sometimes occur and it is necessary to clear them through snaking, rotary-cutter snaking, select digging and pulling, similar methods. In some regions farmers must do continual maintenance of tile drainage lines to keep them open and operating with at least some clearing every year in one or another part of the system.
The ancient Roman authors Cato the Elder and Pliny the Elder described tile drainage systems in 200 BC and the first century AD, respectively. According to the Johnston Farm, tile drainage was first introduced
A tile is a thin object square or rectangular in shape. Tile is a manufactured piece of hard-wearing material such as ceramic, metal, baked clay, or glass used for covering roofs, walls, or other objects such as tabletops. Alternatively, tile can sometimes refer to similar units made from lightweight materials such as perlite and mineral wool used for wall and ceiling applications. In another sense, a tile is a construction tile or similar object, such as rectangular counters used in playing games; the word is derived from the French word tuile, which is, in turn, from the Latin word tegula, meaning a roof tile composed of fired clay. Tiles are used to form wall and floor coverings, can range from simple square tiles to complex or mosaics. Tiles are most made of ceramic glazed for internal uses and unglazed for roofing, but other materials are commonly used, such as glass, cork and other composite materials, stone. Tiling stone is marble, granite or slate. Thinner tiles can be used on walls than on floors, which require more durable surfaces that will resist impacts.
Decorative tilework or tile art should be distinguished from mosaic, where forms are made of great numbers of tiny irregularly positioned tesserae, each of a single color of glass or sometimes ceramic or stone. The earliest evidence of glazed brick is the discovery of glazed bricks in the Elamite Temple at Chogha Zanbil, dated to the 13th century BC. Glazed and colored bricks were used to make low reliefs in Ancient Mesopotamia, most famously the Ishtar Gate of Babylon, now reconstructed in Berlin, with sections elsewhere. Mesopotamian craftsmen were imported for the palaces of the Persian Empire such as Persepolis; the use of sun-dried bricks or adobe was the main method of building in Mesopotamia where river mud was found in abundance along the Tigris and Euphrates. Here the scarcity of stone may have been an incentive to develop the technology of making kiln-fired bricks to use as an alternative. To strengthen walls made from sun-dried bricks, fired bricks began to be used as an outer protective skin for more important buildings like temples, city walls and gates.
Making fired. Fired bricks are solid masses of clay heated in kilns to temperatures of between 950° and 1,150°C, a well-made fired brick is an durable object. Like sun-dried bricks they were made in wooden molds but for bricks with relief decorations special molds had to be made. Rooms with tiled floors made of clay decorated with geometric circular patterns have been discovered from the ancient remains of Kalibangan and AhladinoTiling was used in the second century by the Sinhalese kings of ancient Sri Lanka, using smoothed and polished stone laid on floors and in swimming pools. Historians consider the techniques and tools for tiling as well advanced, evidenced by the fine workmanship and close fit of the tiles. Tiling from this period can be seen in Ruwanwelisaya and Kuttam Pokuna in the city of Anuradhapura; the Achaemenid Empire decorated buildings with glazed brick tiles, including Darius the Great's palace at Susa, buildings at Persepolis. The succeeding Sassanid Empire used tiles patterned with geometric designs, plants and human beings, glazed up to a centimeter thick.
Early Islamic mosaics in Iran consist of geometric decorations in mosques and mausoleums, made of glazed brick. Typical turquoise tiling becomes popular in 10th-11th century and is used for Kufic inscriptions on mosque walls. Seyyed Mosque in Isfahan, Dome of Maraqeh and the Jame Mosque of Gonabad are among the finest examples; the dome of Jame' Atiq Mosque of Qazvin is dated to this period. The golden age of Persian tilework began during the reign the Timurid Empire. In the moraq technique, single-color tiles were cut into small geometric pieces and assembled by pouring liquid plaster between them. After hardening, these panels were assembled on the walls of buildings, but the mosaic was not limited to flat areas. Tiles were used to cover both the exterior surfaces of domes. Prominent Timurid examples of this technique include the Jame Mosque of Yazd, Goharshad Mosque, the Madrassa of Khan in Shiraz, the Molana Mosque. Other important tile techniques of this time include girih tiles, with their characteristic white girih, or straps.
Mihrabs, being the focal points of mosques, were the places where most sophisticated tilework was placed. The 14th-century mihrab at Madrasa Imami in Isfahan is an outstanding example of aesthetic union between the Islamic calligrapher's art and abstract ornament; the pointed arch, framing the mihrab's niche, bears an inscription in Kufic script used in 9th-century Qur'an. One of the best known architectural masterpieces of Iran is the Shah Mosque in Isfahan, from the 17th century, its dome is a prime example of tile mosaic and its winter praying hall houses one of the finest ensembles of cuerda seca tiles in the world. A wide variety of tiles had to be manufactured in order to cover complex forms of the hall with consistent mosaic patterns; the result was a technological triumph as well as a dazzling display of abstract ornament. During the Safavid period, mosaic ornaments were replaced by a haft rang technique. Pictures were painted on plain rectangle tiles and fired afterwards. Besides economic reasons, the seven colors method gave more freedom to artists and was less time-consuming.
It was popular until the Qajar period, when the palette of colors was extended by orange. The seven colors of Haft Rang tiles were black, ultramarine
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to a variety of geometries. A periodic tiling has a repeating pattern; some special kinds include regular tilings with regular polygonal tiles all of the same shape, semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes. In the geometry of higher dimensions, a space-filling or honeycomb is called a tessellation of space. A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons; such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings.
Tessellations were used in Ancient Rome and in Islamic art such as in the decorative geometric tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs. Tessellations were used by the Sumerians in building wall decorations formed by patterns of clay tiles. Decorative mosaic tilings made of small squared blocks called tesserae were employed in classical antiquity, sometimes displaying geometric patterns. In 1619 Johannes Kepler made an early documented study of tessellations, he wrote about semiregular tessellations in his Harmonices Mundi. Some two hundred years in 1891, the Russian crystallographer Yevgraf Fyodorov proved that every periodic tiling of the plane features one of seventeen different groups of isometries.
Fyodorov's work marked the unofficial beginning of the mathematical study of tessellations. Other prominent contributors include Aleksei Shubnikov and Nikolai Belov, Heinrich Heesch and Otto Kienzle. In Latin, tessella is a small cubical piece of stone or glass used to make mosaics; the word "tessella" means "small square". It corresponds to the everyday term tiling, which refers to applications of tessellations made of glazed clay. Tessellation in two dimensions called planar tiling, is a topic in geometry that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules; these rules can be varied. Common ones are that there must be no gaps between tiles, that no corner of one tile can lie along the edge of another; the tessellations created by bonded brickwork do not obey this rule. Among those that do, a regular tessellation has both identical regular tiles and identical regular corners or vertices, having the same angle between adjacent edges for every tile.
There are only three shapes that can form such regular tessellations: the equilateral triangle and regular hexagon. Any one of these three shapes can be duplicated infinitely to fill a plane with no gaps. Many other types of tessellation are possible under different constraints. For example, there are eight types of semi-regular tessellation, made with more than one kind of regular polygon but still having the same arrangement of polygons at every corner. Irregular tessellations can be made from other shapes such as pentagons, polyominoes and in fact any kind of geometric shape; the artist M. C. Escher is famous for making tessellations with irregular interlocking tiles, shaped like animals and other natural objects. If suitable contrasting colours are chosen for the tiles of differing shape, striking patterns are formed, these can be used to decorate physical surfaces such as church floors. More formally, a tessellation or tiling is a cover of the Euclidean plane by a countable number of closed sets, called tiles, such that the tiles intersect only on their boundaries.
These tiles may be any other shapes. Many tessellations are formed from a finite number of prototiles in which all tiles in the tessellation are congruent to the given prototiles. If a geometric shape can be used as a prototile to create a tessellation, the shape is said to tessellate or to tile the plane; the Conway criterion is a sufficient but not necessary set of rules for deciding if a given shape tiles the plane periodically without reflections: some tiles fail the criterion but still tile the plane. No general rule has been found for determining if a given shape can tile the plane or not, which means there are many unsolved problems concerning tessellations. Mathematically, tessellations can be extended to spaces other than the Euclidean plane; the Swiss geometer Ludwig Schläfli pioneered this by defining polyschemes, which mathematicians nowadays call polytopes. These are the analogues to polygons and polyhedra in spaces with more dimensions, he further defined the Schläfli symbol notation to make it easy to describe polytopes.
For example, the Schläfli symbol for an equilateral triangle is. The Schläfli notation makes it possible to describe tilings compactly. For example, a tiling of regular hexagons has three six-sided polygons at each vertex, so its Schläfli symbol is. Other methods exist for describing polygonal tilings; when the tessellation
Heinrich Sylvester Theodor Tiling
Heinrich Sylvester Theodor Tiling was a German–Russian physician and naturalist. During his years he became an American citizen, his parents were née Pearson of Balmadis. He studied medicine in Dorpat from 1838 to 1844, he graduated and received a doctor's degree in 1844. Tiling became a physician at the "Russian North American Co." in Ayan, Siberia from 1845 through 1851. He went to Ayan over land with his young wife and arrived in winter 1845; the difficulties during the overland journey were extreme in parts. He published an account of it in Eine Reise um die Welt... See below; the German title of the book translates as: "A journey around the world from West to East through Siberia and the Pacific and Atlantic seas". During his time in Ayan, he kept a daily register of rainfall for Ayan, he described all plants in the area and published an account of it with the director of the botanical gardens in St. Petersburg, Eduard August von Regel, he went back to Riga with his wife and four small children and arrived early 1852.
After that, he practiced medicine in Riga from 1853–1854. From 1854 to 1863, he practiced in Wenden and from 1863 in Sitka, Alaska, he had settled in Sitka before the Alaska purchase. After it he stayed and went on to San Francisco and Nevada City, California, he collected and described numerous plants and species in Siberia and California from 1844 to 1871 such as Tiling's monkeyflower, Mimulus tilingii, native to North America. Directly after having got the doctor's degree, he was offered a post with the Russian-American Company to become the company surgeon in their newly created port on the Ochotsk Sea, Ayan, he married in the spring of 1844 Anna Elisabeth Fehrmann. She accompanied him on the overland journey to Siberia. Tiling started to learn the Russian language during his travels; the journey was slow and lasted longer than planned and it was winter when they arrived. After a lot of trouble that ended nearly deadly, they arrived in Ayan on 4 December 1844 and Tiling began his work. At the time of his arrival, Ayan had only about 100 inhabitants and his duties as a doctor took up only about an hour per day.
Thus Tiling could spend most of the day making scientific observations. One example is the temperature tables he made starting November 1847, he took temperatures three times per day, at 7 a.m. 2 p.m. and 9 pm, calculated monthly median values, monthly high and low temperatures. He logged cloud cover, barometer readings, wind direction, rainfall, he collected plants in the near vicinity of Ayan and according to his own conclusion "hardly missed one". His weather readings for Ayan are the oldest in Eastern Siberia; the flora of Ayan is one of the best documented in Siberia. In 1851, he and his family, now with four little children, took the boat from Ayan to Sachalin, Sitka, Tahiti, around Cape Horn through the Atlantic Ocean back to Kronstadt. After the arrival in Europe, Tiling practised first in Riga. In 1854 he was the county surgeon for Wenden. Only when he moved to America he left this post. From 1863 to 1868, Tiling was surgeon in Alaska; this was either again with the Russian-American Company, or with the Russian Government represented through the governor.
Whether his wife and family accompanied him on this second journey is not clear, yet it is likely. She herself died in Riga in 1876, much all their eight children. So nobody of the family stayed in the end in North America. At the time of the journey their youngest child Eduard was only six years old. Therefore, it can be assumed that at least some of the children came with him. In 1867 the US government purchased Alaska from Russia. Most of the higher ranking Russian officials moved back to Europe, it is likely that Tiling spoke English, his mother being English. His wife Anna was born in London and should have some degree of knowledge of the English language as well. There is no detailed written evidence about the movements to San Francisco and Nevada City; the collection and categorization of plants is core to Tiling’s personality. This passion is with him throughout his life. From his various places of residence he send back plants, specimens and descriptions. Lange and Gumprecht, the two persons that reviewed Eine Reise um die Welt....
Sing his praise for the introduction and popularisation of the pretty garden shrub Weigela Middendorfiana to Europe's gardens. In addition to that Regel wrote: "It is Dr. Tiling to whom we owe the introduction of many excellent Siberian plants" The review of Lange and Gumprecht go far above a normal book review, they add information about Tilings voyage, not contained in the book they review. The size of the review with 21 full pages is remarkable as well. Although Eine Reise um die Welt was published anonymously the reviewers did know the author and supported his views. At least among the German speaking people "in the know" it was clear who the author of Eine Reise um die Welt was. There reviewers previously. Intensive was Tilings exchange with the director of the Botanical Gardens in St Petersburg, Eduard August von Regel with whom he published Florula Ajanensis. Trained as a medical man and having the collection of plants at his heart his interests far exceeded these two areas. One example is the meteorological observations in Ayan described above.
This is the earliest systematic weather observations taken in Eastern Siberia. Through the scientifically trained experience of di
Brickwork is masonry produced by a bricklayer, using bricks and mortar. Rows of bricks—called courses— are laid on top of one another to build up a structure such as a brick wall. Bricks may be differentiated from blocks by size. For example, in the UK a brick is defined as a unit having dimensions less than 337.5x225x112.5mm and a block is defined as a unit having one or more dimensions greater than the largest possible brick. Brick is a popular medium for constructing buildings, examples of brickwork are found through history as far back as the Bronze Age; the fired-brick faces of the ziggurat of ancient Dur-Kurigalzu in Iraq date from around 1400 BC, the brick buildings of ancient Mohenjo-daro in Pakistan were built around 2600 BC. Much older examples of brickwork made with dried bricks may be found in such ancient locations as Jericho in Judea, Çatal Hüyük in Anatolia, Mehrgarh in Pakistan; these structures have survived from the Stone Age to the present day. Brick dimensions are expressed in construction or technical documents in two ways as co-ordinating dimensions and working dimensions.
Coordination dimensions are the actual physical dimensions of the brick with the mortar required on one header face, one stretcher face and one bed. Working dimensions is the size of a manufactured brick, it is called the nominal size of a brick. Brick size may be different due to shrinkage or distortion due to firing etc. An example of a co-ordinating metric used for bricks in the UK is as follows: Bricks of dimensions 215 mm × 102.5 mm × 65 mm. In this case the co-ordinating metric works because the length of a single brick is equal to the total of the width of a brick plus a perpend plus the width of a second brick. There are many other brick sizes worldwide, many of them use this same co-ordinating principle; as the most common bricks are cuboids, six surfaces are named as followed: Top and bottom surfaces are called Beds Ends or narrow surfaces are called Headers or header faces Sides or wider surfaces are called Stretchers or stretcher faces Mortar placed between bricks is given separate names with respect to their position.
Mortar placed horizontally below or top of a brick is called a bed, mortar Placed vertically between bricks is called a perpend. A brick made with just rectilinear dimensions is called a solid brick. Bricks might have a depression on a single bed; the depression is called a frog, the bricks are known as frogged bricks. Frogs should never exceed 20 % of the total volume of the brick. Cellular bricks have depressions exceeding 20% of the volume of the brick. Perforated bricks have holes through the brick from bed to bed. Most of the building standards and good construction practices recommend the volume of holes should not exceeding 20% of the total volume of the brick. Parts of brickwork include bricks and perpends; the bed is the mortar upon. A perpend is a vertical joint between any two bricks and is usually—but not always—filled with mortar. A brick is given a classification based on how it is laid, how the exposed face is oriented relative to the face of the finished wall. Stretcher or stretching brick A brick laid flat with its long narrow side exposed.
Header or heading brick A brick laid flat with its width exposed. Soldier A brick laid vertically with its long narrow side exposed. Sailor A brick laid vertically with the broad face of the brick exposed. Rowlock A brick laid on the long narrow side with the short end of the brick exposed. Shiner or rowlock stretcher A brick laid on the long narrow side with the broad face of the brick exposed; the practice of laying uncut full-sized bricks wherever possible gives brickwork its maximum possible strength. In the diagrams below, such uncut full-sized bricks are coloured as follows: Stretcher HeaderOccasionally though a brick must be cut to fit a given space, or to be the right shape for fulfilling some particular purpose such as generating an offset—called a lap—at the beginning of a course. In some cases these special shapes or sizes are manufactured. In the diagrams below, some of the cuts most used for generating a lap are coloured as follows: Three-quarter bat, stretching A brick cut to three-quarters of its length, laid flat with its long, narrow side exposed.
Three-quarter bat, heading A brick cut to three-quarters of its length, laid flat with its short side exposed. Half bat A brick cut in half across its length, laid flat. Queen closer A brick cut in half down its width, laid with its smallest face exposed and standing vertically. A queen closer is used for the purpose of creating a lap. Less used cuts are all coloured as follows: Quarter bat A brick cut to a quarter of its length. Three-quarter queen closer A queen closer cut to three-quarters of its length. King closer A brick with one corner cut away. A nearly universal rule in brickwork is. Walls, extending upwards, can be of varying depth or thickness; the bricks are laid running linearly and extending upwards, forming wythes or leafs. It is as important; the dominant method for consolidating the leaves together was to lay bricks across them, rather than running linearly. Brickwork observing either or both of these two conventions is described as being laid in one or another bond. A leaf is as thick as the width of one brick, but a wall is said to be one brick thick if it as wide as the length of a brick.
Accordingly, a single-leaf wall