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Abstract ruler in which some of the distance marks may be missing
A sparse ruler is a ruler in which some of the distance marks may be missing. More abstractly, a sparse ruler of length L {\displaystyle L} with m {\displaystyle
Sparse_ruler
Set of marks along a ruler such that no two pairs of marks are the same distance apart
Costas array Volunteer computing BOINC distributed.net Perfect ruler Sidon sequence Sparse ruler Sidon, S. (1932). "Ein Satz über trigonometrische Polynome
Golomb_ruler
{\displaystyle 4=7-3} Golomb ruler Sparse ruler All-interval tetrachord This article incorporates material from perfect ruler on PlanetMath, which is licensed
Perfect_ruler
BC – 494 AD) ruled in modern-day Northeast China. Although records are sparse and contradictory, it is speculated that in the 1st century BC, Eastern
List_of_monarchs_of_Korea
Type of graph vertex labeling
\left\lceil {\sqrt {3m+{\tfrac {9}{4}}}}\right\rfloor } vertices, due to sparse ruler results. This conjecture has been verified for all graphs with 213 or
Graceful_labeling
American rapper and record producer (born 1969)
and those of its members. Known for his signature use of soul samples, sparse beats, and cinematic elements, his production style has been widely influential
RZA
Centers of power for the Maya civilization
Balam (Note:Despite the sparse references to previous rulers in Copán, the first safe reference is from 426. All the rulers, with the exception of the
Maya_monarchs
Alliance of three Nahua city states in Mexico (1428–1521)
peoples, who migrated to central Mexico from the north (mainly centered sparsely around present-day states of Zacatecas, San Luis Potosí, and Guanajuato)
Aztec_Empire
Identification of emperors with divine authority
of apotheosis served religious, political and moral judgment on Imperial rulers and allowed living emperors to associate themselves with a well-regarded
Roman_imperial_cult
Periodic sequence of integers whose partial sums are triangular numbers
Šindel sequence with period sum s {\displaystyle s} is not trivial. Sparse ruler Křížek, Somer & Šolcová (2021), Equation 10.5, p. 229. Křížek, Somer
Šindel_sequence
Medieval Muslim empire (c. 1077–1231)
Qara Khitai (Western Liao dynasty), and from circa 1190 as independent rulers up until the Mongol invasion in 1219–1221. The date of the founding of the
Khwarazmian_Empire
Ancient Mesopotamian city-state
evidence from this period is sparse and predominately come from religious buildings. Material culture from this era is sparse, but a few inscriptions reveal
Ur
Ethnic group of central Mexico and its civilization
rather dominated its client city-states primarily by installing friendly rulers in conquered territories, constructing marriage alliances between the ruling
Aztecs
king of Assyria (Akkadian: Iššiʾak Aššur, later šar māt Aššur) was the ruler of the ancient Mesopotamian kingdom of Assyria, which was founded in the
List_of_Assyrian_kings
Disputed territory in north-western Africa
around 600,000 inhabitants, it is the most sparsely populated territory in Africa and the second most sparsely populated territory in the world after Greenland
Western_Sahara
Mann and the Isles", although only some of the later rulers claimed that title. At times the rulers were independent of external control, although for much
List of rulers of the Kingdom of the Isles
List_of_rulers_of_the_Kingdom_of_the_Isles
2017 studio album by Christian Scott
Ruler Rebel is a studio album by American jazz trumpeter Christian Scott released on March 31, 2017 by Ropeadope Records. The album is the first installment
Ruler_Rebel
Dense collection of trees covering a relatively large area
herbivory are recurrent phenomena, savannas develop. Sparse trees and savanna are forests with sparse tree-canopy cover. They occur principally in areas
Forest
Empire in West Africa from c. 200s to c. 1200s
The word Ghana means warrior or war chief, and was the title given to the rulers of the kingdom. Kaya Maghan (king of gold) was another title for these kings
Ghana_Empire
Narrow strait in northwestern Turkey
shores of the strait along the Gallipoli peninsula (Turkish: Gelibolu) are sparsely settled, while the southern shores along the Troad peninsula (Turkish:
Dardanelles
Military estate of East Slavic people
the word Cossack(s) into three groups: Late 14th – early 15th century: Sparse references to individual Cossacks. Late 15th – early 16th century: Cossacks
Cossacks
Ethnic group
matters. There is considerable Mixtec documentation for land issues, but sparse for market activity, perhaps because Indigenous cabildos did not regulate
Mixtec
State in Islamic Iberia (756–1031 CE)
of Mérida. Ethnic Arabs were (at least during the early Emirate period) sparse here and the Muslim population consisted mostly of Berbers, probably semi-nomadic
Umayyad_state_of_Córdoba
Domestic species of mammal
since ancient times, but there is widespread disagreement because of the sparseness of written accounts and the inconsistency of those which survive. Contemporary
Ferret
Monarchical and political regime of parts of the Netherlands from 1384 to 1482
the political system of relatively petty lords was ending, and stronger rulers (with actual power over larger territories) started to emerge. In the case
Burgundian_Netherlands
Historic kingdom in Sub-Roman Britain
6th century as a pun on "damnation" to deprecate the area's contemporary ruler Constantine. The name etymologically originates from Proto-Celtic *dubno-
Dumnonia
National god of the Babylonians
Tiberian: Mərōḏaḵ) was a god from ancient Mesopotamia, patron deity of Babylon. First sparsely attested in the 3rd millennium BC, Marduk slowly rose to prominence before
Marduk
One of three political entities which controlled Okinawa during Sanzan period
country, a kingdom, or a principality by modern historians, however the rulers of Hokuzan were in fact not "kings" at all, but petty lords with their own
Hokuzan
1947 division of British India
the British withdrew from their obligations to the states, leaving the rulers to decide whether to accede to India or Pakistan or to remain independent
Partition_of_India
various events, rulers and dynasties. Historical inscriptions and texts customarily record events in terms of a succession of officials or rulers: "in the year
Chronology of the ancient Near East
Chronology_of_the_ancient_Near_East
11th century BC precursor to the Zhou dynasty
Zhou dynasty). However, the records detailing the former's rule are very sparse, so modern historiography has generally been more concerned about precisely
Predynastic_Zhou
Type of matrix factorization
algorithms have been developed for factorizing large sparse matrices. These algorithms attempt to find sparse factors L and U. Ideally, the cost of computation
LU_decomposition
Dynasty of ancient Egypt (Old Kingdom)
Achês (Huni). The archaeological evidence shows that Khasekhemwy, the last ruler of the Second Dynasty, was succeeded by Djoser, who at the time was only
Third_Dynasty_of_Egypt
Largest city in Switzerland
station are the largest and busiest in the country. Evidence of early, sparse settlements in the area dates back more than 6,400 years, indicating human
Zurich
Country within the United Kingdom
an abrupt halt in the previous sheep farming boom. Scotland is the most sparsely populated country of the United Kingdom. In August 2012, the Scottish population
Scotland
Country within the United Kingdom
Wrexham being the largest northern city. The remaining parts of Wales are sparsely populated. Since the decline of the country's traditional extractive and
Wales
Region in South Asia
the Treaty of Amritsar, the Raja of Jammu, Gulab Singh, became the new ruler of Jammu and Kashmir. The rule of his descendants, under the paramountcy
Kashmir
Island and historical province in Sweden
distance from road connections. Slite is the largest settlement on Gotland's sparsely populated east coast. The eastern coast of Gotland, including the adjacent
Gotland
Country in Eastern Europe and North Asia
square kilometre (22 inhabitants/mi2), Russia is one of the world's most sparsely populated countries, with the vast majority of its people concentrated
Russia
State in Germany
west of Lower Saxony is the Emsland, an economically emerging but rather sparsely populated area, once dominated by inaccessible swamps. The northern half
Lower_Saxony
7th-century British queen of Northumbria
Alhflaed. According to British sources a friendly connection between the rulers of Rheged and Northumbria predated Rhiainfellt's marriage, as her grandfather
Rhiainfellt
Country in Southern and Western Europe
Oscan: Víteliú). Several ancient authors said it was named after a local ruler Italus. The ancient Greek term for Italy initially referred only to the
Italy
Lion population in India
from the females by the presence of manes, though they are shorter and sparser than the African counterparts. It also differs from the African lion in
Asiatic_lion
South Indian dynasty (1163–1323)
Odisha. Their capital was Orugallu, now known as Warangal. Early Kakatiya rulers served as feudatories to Rashtrakutas and Western Chalukyas for over two
Kakatiya_dynasty
Ancient Maya city-state in Chiapas, Mexico
A list of possible and known Maya rulers of the city, with dates of their reigns: Mythological and legendary rulers: ?-Muwaan Mat c.2325 BC Ukʼix Chan
Palenque
religion extend into prehistory, though evidence for them comes only from the sparse and ambiguous archaeological record. Careful burials during the Predynastic
Ancient_Egyptian_religion
State of Mexico
estimated population of 3,769,020 as of 2020, significantly higher than the sparsely populated Baja California Sur to the south, and similar to San Diego County
Baja_California
7th–15th century political entity
known as Sawankalok. Historical records on Chaliang during this period are sparse. After Sukhothai became the vassal of Ayutthaya, it is speculated that Chaliang
Mueang_Chaliang
972 battle between Mieszko I of Poland and Odo I of Lusatia
possession of the area between Mieszko and Odo. Records of the battle are sparse, it was briefly described by the chronicler Thietmar of Merseburg (975−1018)
Battle_of_Cedynia
Macedonian general, Diadochus, and founder of the Seleucid Empire
struggles following Alexander's death, Seleucus rose to become the total ruler of Asia Minor, Syria, Mesopotamia, and the Iranian plateau, assuming the
Seleucus_I_Nicator
Former country (1247-1330), now a part of modern-day Romania
earliest possible ruler of Țara Litua. He was mentioned by Rashid al-Din Hamadani in Jami' al-tawarikh (1241), described as the ruler of Ilaut (Oltenia)
Țara_Litua
Barbarian invasions against the Roman Empire in the 3rd century
difficult by having to garrison immense stretches of frontier with mostly sparse military contingents. Many of the emperors who were gradually proclaimed
Barbarian invasions into the Roman Empire of the 3rd century
Barbarian_invasions_into_the_Roman_Empire_of_the_3rd_century
Jewish kingdom in the southern Levant (140–37 BC)
the end of Judea's independence. Hyrcanus II was installed as a client ruler, though his authority was contested by his younger brother Aristobulus II
Hasmonean_Judea
Country in North Africa
Egypt then became part of the Ottoman Empire in 1517, until its local ruler Muhammad Ali established modern Egypt as an autonomous Khedivate in 1867
Egypt
1040–1147 Berber dynasty in west Africa and Iberia
of Islamic art globally, and of the contributions of the Almoravids as "sparse" as a result of the empire's "puritanical fervour" and "ephemerality." At
Almoravid_dynasty
Large permanent human settlement
potential to have a smaller ecological footprint per inhabitant than more sparsely populated areas. Therefore, compact cities are often referred to as a crucial
City
1686, the Council of Virginia was informed of the death of Cockacoeske, ruler of the Pamunkey for 30 years: George Smith Interpreter to ye Pomunkey [Pamunkey]
Queen_Betty
1526–1857 empire in South Asia
Empire is conventionally said to have been founded in 1526 by Babur, a ruler from what is now Uzbekistan, who with the help of the neighbouring Safavid
Mughal_Empire
Italian cardinal deacon (1475–1507)
and his Italian mistress Vannozza dei Cattanei, about whom information is sparse. He had three full siblings: Giovanni Borgia, Lucrezia Borgia and Gioffre
Cesare_Borgia
State in South Asia (1748–1955)
lived on the fertile Indus River banks with the eastern desert tract being sparsely populated. Between 1916 and 1941, the population had almost doubled due
Bahawalpur_(princely_state)
Founder of the Akkadian Empire
romanized: Šarrugi; died c. 2279 BC), also known as Sargon the Great, was the first ruler of the Akkadian Empire, known for his conquests of the Sumerian city-states
Sargon_of_Akkad
Sultan of the Ottoman Empire from 1648 to 1687
Köprülü era. Mehmed IV was known by contemporaries as a particularly pious ruler, and was referred to as gazi, or "holy warrior" for his role in the many
Mehmed_IV
Country in Central and Southeast Europe
72.9 inhabitants per square kilometre, making Croatia one of the more sparsely populated European countries. The overall life expectancy in Croatia at
Croatia
The kings of Elam were the rulers of Elam, an ancient civilization and kingdom in south-western Iran. The earliest known Elamite dynasty was the Awan dynasty
List_of_Elamite_kings
Ethnic groups who speak the Mande languages
Mandé-speaking peoples inhabit various environments, from coastal rainforests to the sparse Sahel, and have a wide range of cuisines, cultures, and beliefs. After migrating
Mandé_peoples
Norse-Gaelic polity in the British Isles (849–1265)
were nominally under Pictish control although the historical record is sparse. According to Ó Corráin (1998) "when and how the Vikings conquered and occupied
Kingdom_of_the_Isles
Country in East Asia
inland sea. With a population of 3.5 million, Mongolia is the world's most sparsely populated sovereign state, excluding partially unrecognized Western Sahara
Mongolia
Country in Northwestern Europe and the Caribbean
Hague and comprised representatives from each of the seven provinces. The sparsely populated region of Drenthe was part of the republic, albeit not considered
Netherlands
Hereditary king of kingdom of Calicut (1124–1806)
Samorim, Dutch: Samorijn, Chinese: Shamitihsi) was the title of the erstwhile ruler and monarch of the Calicut kingdom in the South Malabar region of India
Zamorin
Ancient Hurrian-speaking state in northern Syria and southeast Anatolia
have yet been found in its excavated sites, knowledge about Mitanni is sparse compared to the other powers in the area, and dependent on what its neighbours
Mitanni
c. 880–1240 East Slavic state in Europe
uniting the East Slavic tribes. According to the Primary Chronicle, the first ruler to unite East Slavic lands into what would become Kievan Rus' was Varangian
Kievan_Rus'
Ethnic group in West Africa
a culturally homogeneous people based primarily in the Sahelian and the sparse savanna areas of southern Niger and northern Nigeria respectively, numbering
Hausa_people
Ancient Semitic-speaking people from the Levant
not known to what extent these reflect historical facts. There are also sparse mentions about Amorites (often as MAR-DUki) in tablets from the East Semitic-speaking
Amorites
5th–8th-century nomadic confederation in Central Asia
expanded into Northern India as well. The sources for Hephthalite history are sparse and the opinions of historians differ. There is no king-list, and historians
Hephthalites
Ancient state in West Asia
Ashurbanipal’s reign (r. 668–630 BCE), references to the Medes become very sparse. Ashurbanipal reports that three Median city lords had rebelled against
Median_kingdom
East Asian ethnic group
settlement by Chinese of lands previously regarded as part of the empire's sparsely populated frontier or periphery. Guangdong and Fujian, hitherto regarded
Han_Chinese
Ancient Egyptian dynasty
Period owing to the ephemeral nature of its kings' reigns as well as the sparsity of contemporary evidence, hinting at a decline of the state into chaos
Eighth_Dynasty_of_Egypt
Ancient Roman city in Germany
in late antiquity: between the late 3rd and late 4th centuries several rulers, including Constantine the Great, used the city as one of the western imperial
Augusta_Treverorum
1965 science fiction novel by Frank Herbert
stewardship of the planet Arrakis. While the planet is an inhospitable and sparsely populated desert wasteland, it is the only source of melange or "spice"
Dune_(novel)
Ancient Egyptian dynasty
may have included Canaan itself, although the archaeological record is sparse. The dynasty probably lasted for a period of about 108 years. The first
Fifteenth_Dynasty_of_Egypt
Country in Central Asia
population of the Central Asian republics while being one of the most sparsely populated nations located on the Asian continent. Turkmenistan has long
Turkmenistan
2021 video game
in packs, forcing the player to rethink their strategy on whether to use sparse ammunition, use melee combat, or run away. Similar to Resident Evil 4 (2005)
Resident_Evil_Village
Autonomous community of Spain
colonisation process undertaken by the new Castilian rulers. This underpinned the features of a sparse population in the region; as a result, ranching became
Castilla–La_Mancha
2006 video game
original release, opportunities to recover health during the trial are sparse. Other Zelda-related Amiibo figurines have distinct functions: Link and
The Legend of Zelda: Twilight Princess
The_Legend_of_Zelda:_Twilight_Princess
Indian Freedom Fighter (1831 – 1858)
British East India Company during the 1857 rebellion, her information is sparse and mostly comes from folklore. In the 21st century, she has been used as
Avantibai
Ancient Iranian civilization (6th century BCE – 11th century CE)
founder of the Achaemenid Empire, and then was annexed by the Macedonian ruler Alexander the Great in 328 BC. It would continue to change hands under the
Sogdia
Iran under the Safavid dynasty from 1501 to 1736
thought was in stark contrast to Europe. He blamed this on misgovernment, the sparse population of the country, and lack of appreciation of agriculture amongst
Safavid_Iran
Early medieval cultural group in Britain
"it does not follow that the 10th century is better understood than more sparsely documented periods". During the course of the 10th century, the West Saxon
Anglo-Saxons
Edible seeds of Salvia hispanica or related
contaminants, and microbiological criteria. Preliminary research remains sparse and inconclusive. In a 2015 systematic review, most of the studies did not
Chia_seed
Country in northern Europe
has sent athletes to compete in every Games since then, except for the sparsely attended 1904 Games and the 1980 Summer Olympics in Moscow when they participated
Norway
American physician, lawyer, journalist, and mercenary (1824–1860)
enjoyed the support of some important sectors within Nicaraguan society. As ruler of Nicaragua, Walker relegalized slavery, with the goal of creating a new
William_Walker_(filibuster)
located south of Prescott, Arizona, in the United States. This area of sparsely populated pine-covered mountains provides a dark southern sky for the Prescott
Meanings of minor-planet names: 8001–9000
Meanings_of_minor-planet_names:_8001–9000
used as garden plots. The Gilgen and Hasenpfuhl suburbs were even less sparsely settled and the secularised monastery of St. Magdalen stood totally detached
History_of_Speyer
Major Mesopotamian civilization
Assyrian period the deity was considered the formal king of Assur; the actual rulers only used the style Išši'ak ("governor"). From the time of Assyria's rise
Assyria
Crusaders. This had a long-term effect on those areas, which remained sparsely populated for centuries. The activity in that time concentrated more inland
History_of_Israel
be repeated, virtually nothing of use to the historian emerges from the sparse record of the early life of the founder of the latest of the great world
History_of_Islam
Contemporary historiography of the Crusades
Minor works. Other works that are limited in scope, highly derivative or sparsely cited are listed below. Expeditio contra Turcos. by an anonymous author
List of sources for the Crusades
List_of_sources_for_the_Crusades
Historical region in Central Anatolia, Turkey
continental climate, with hot, dry summers and cold, snowy winters. Rainfall is sparse and the region is largely semi-arid.[citation needed] Cappadocia contained
Cappadocia
Mai of the Kanem–Bornu Empire
bin ʿAbd al-Jalīl), called Dunama Dibalemi and Dunama Selmami, was mai (ruler) of the Kanem–Bornu Empire in the early-to-mid 13th century, ruling approximately
Dunama_II_Dibalemi
City in southeastern Uzbekistan
with temperatures reaching and exceeding 40 °C (104 °F). Precipitation is sparse from June through October, but increases to a maximum from February to April
Samarkand
SPARSE RULER
SPARSE RULER
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Surname or Lastname
English
English : patronymic from Spire 1.
Surname or Lastname
English
English : variant of Sparks.
Surname or Lastname
English
English : variant of Spear.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Feel; Healthy; Touch
Surname or Lastname
Portuguese
Portuguese : occupational name from soeiro ‘swineherd’, Latin suerius.English : patronymic from a nickname for someone with reddish hair, from Anglo-Norman French sor ‘chestnut (color)’.
Surname or Lastname
English (Suffolk)
English (Suffolk) : unexplained.
Surname or Lastname
English
English : variant of Speake.
Male
English
Short form of English unisex Paisley, PAISE means "church."Â
Boy/Male
Afghan, Arabic, Iranian, Muslim, Parsi
Pious; Pure; Chaste; Holy
Boy/Male
Anglo Saxon Welsh
Spares.
Female
English
English variant form of French Cerise, SHARISE means "cherry."Â
Surname or Lastname
Irish (Kerry)
Irish (Kerry) : Anglicized form of Gaelic Mac Saoghair, which in turn may be a patronymic from a Gaelicized form of the Old English personal name Saeger (see 2 below).English : patronymic from a Middle English personal name Saher or Seir (see Sayer 1).Americanized form of French Cyr.Richard Sears came to Plymouth, MA, from England about 1630.
Girl/Female
Hindu, Indian
Touch
Boy/Male
American, British, English
Gallant
Surname or Lastname
English
English : patronymic from Spear.
Surname or Lastname
English
English : variant spelling of Pass.French : possibly a nickname from passe ‘sparrow’.
Surname or Lastname
English
English : patronymic from Spark 1.
Surname or Lastname
English
English : from the Norman personal name Serlo, Germanic Sarilo, Serilo. This was probably originally a byname cognate with Old Norse Sorli, and akin to Old English searu ‘armor’, meaning perhaps ‘defender’, ‘protector’.
Surname or Lastname
English
English : metonymic occupational name for someone who made bags or purses or for an official in charge of expenditure, from Middle English purse (via Old English from Latin bursa).Scottish : variant of Purser.
SPARSE RULER
SPARSE RULER
Boy/Male
Hindu
Brilliant, Ruler, Illuminating
Male
Russian
(Ермолай) Russian form of Greek Hermolaos, YERMOLAI means "people of Hermes."
Boy/Male
Muslim
Rightly guided
Surname or Lastname
English (mainly southern)
English (mainly southern) : metonymic occupational name for a dancer, or a nickname for someone with an odd gait, from Middle English trip(p)(en) ‘to step lightly, skip, or hop’ (Old French triper).English : metonymic occupational name for a butcher or tripe dresser, from Middle English, Old French trip(p)e ‘tripe’ (of unknown origin).German : metonymic occupational name for a maker of wooden pattens (trippe), a type of raised sole that could be strapped to normal footwear for walking in unpaved muddy streets.
Boy/Male
Indian, Punjabi, Sikh
Unique; Surprised
Surname or Lastname
English
English : unexplained. Perhaps a nickname for a stormy-tempered person. Compare Stark.
Surname or Lastname
English (mainly Yorkshire and central England)
English (mainly Yorkshire and central England) : habitational name from any of the various places named Hatfield, for example in Yorkshire, Nottinghamshire, Herefordshire, Worcestershire, Hertfordshire, and Essex, from Old English hǣð ‘heathland’, ‘heather’ + feld ‘pasture’, ‘open country’.
Girl/Female
Tamil
Anumathi | அணà¯à®®à®¾à®‚தீ
Apane, Consent
Boy/Male
Arthurian Legend
Various names for Arthur's sword.
Male
Hindi/Indian
(दयाराम) Abbreviated form of Hindi Dayarama, DAYARAM means "compassion of Rama."
SPARSE RULER
SPARSE RULER
SPARSE RULER
SPARSE RULER
SPARSE RULER
n.
To emit sparks; to throw off ignited or incandescent particles; to shine as if throwing off sparks; to emit flashes of light; to scintillate; to twinkle; as, the blazing wood sparkles; the stars sparkle.
adv.
Sparsely; scatteredly; here and there.
superl.
Not refined; rough; rude; unpolished; gross; indelicate; as, coarse manners; coarse language.
v. t.
Held in reserve, to be used in an emergency; as, a spare anchor; a spare bed or room.
n.
One who parses.
v. t.
To sift through a sarse.
v. t.
Being over and above what is necessary, or what must be used or reserved; not wanted, or not used; superfluous; as, I have no spare time.
imp. & p. p.
of Parse
imp. & p. p.
of Spare
v. t.
To emit in the form or likeness of sparks.
v. t.
To inclose in a hearse; to entomb.
v. t.
To sprinkle; to moisten by sprinkling; as, to sparge paper.
n.
Brilliancy; luster; as, the sparkle of a diamond.
n.
The right of bowling again at a full set of pins, after having knocked all the pins down in less than three bowls. If all the pins are knocked down in one bowl it is a double spare; in two bowls, a single spare.
v. t.
Scanty; not abundant or plentiful; as, a spare diet.
superl.
Thinly scattered; set or planted here and there; not being dense or close together; as, a sparse population.
n.
One who spares.
adv.
In a scattered or sparse manner.
n.
A fine sieve; a searce.
superl.
Large in bulk, or composed of large parts or particles; of inferior quality or appearance; not fine in material or close in texture; gross; thick; rough; -- opposed to fine; as, coarse sand; coarse thread; coarse cloth; coarse bread.