the-french-artist/wikipedia_20220301.simple_sentence_split huggingface dataset:
It turns out that for this simple problem, the answer is "yes" when we have 6 or more points, no matter how the lines are colored.
But when we have 5 points or fewer, we can color the lines so that the answer is "no".
By asking that the 4 points lie on a plane, we have made the problem much harder.
We would like to know: for what values of n is the answer "no" (for some way of coloring the lines), and for what values of n is it "yes" (for all ways of coloring the lines)?
But this problem has not been completely solved yet.
In 1971, Ronald Graham and B. L. Rothschild found a partial answer to this problem.
They showed that for n=6, the answer is "no".
But when n is very large, as large as Graham's number or larger, the answer is "yes".
One of the reasons this partial answer is important is that it means that the answer is eventually "yes" for at least some large n. Before 1971, we didn't know even that much.
Graham's number, G, G, G, is much larger than N: N: N: f 64 (4), {f^{64}(4)}, f 6 4 (4), where f (n) = 3 ↑ n 3. {
f(n)\;=\;3\↑ ^{n}3}.
f (n) = 3 ↑ n 3.
This weaker upper bound for the problem, attributed to an unpublished work of Graham, was eventually published and named by Martin Gardner in Scientific American in November 1977.
Graham's number is not only too big to write down all of its digits, it is too big even to write in scientific notation.
In order to be able to write it down, we have to use Knuth's up-arrow notation.
We will write down a sequence of numbers that we will call g1, g2, g3, and so on.
Each one will be used in an equation to find the next.
g64 is Graham's number.
is 3x3x3 which equals 27.
An arrow between two numbers just means the first number multiplied by itself the second number of times.
One can think of  as  because two arrows between numbers A and B just means A written down a B number of times with an arrow in between each A. Because we know what single arrows are,  is 3 multiplied by itself  times and we know  is twenty-seven.
So  is 3x3x3x3x....x3x3, in total 27 times.
That equals 7,625,597,484,987.
is  and we know  is 7,625,597,484,987.
So  is .
That can also be written as  with a total of 7,625,597,484,987 3s.
This number is so huge, its digits, even written very small, could fill up the observable universe and beyond.
Although this number may already be beyond comprehension, this is barely the start of  this giant number.
The next step like this is  or .
This is the number we will call g1.
After that, g2 is equal to ; the number of arrows in this number is g1.
g3 is equal to , where the number of arrows is g2.
We keep going in this way.
We stop when we define g64 to be , where the number of arrows is g63.
Laguna City is a little city of south of the Brazil, in Santa Catarina State.
This city have more than 50000 people.
It was the capital of the short-lived Juliana Republic in 1839.
The city is known for having dolphins
Mar Grosso beach
Iró beach
Gravatá beach
Gi beach.
Tak'alik A'baj'  is an ancient ruin in Guatemala; it used to be called Abaj Takalik.
It is one of several Mesoamerican sites that have Olmec and Maya features.
The site was inhabited the during the Preclassic and Classic periods, from the 9th century BC through to at least the 10th century AD.
It was an important place for trade.
It traded with Kaminaljuyu and Chocolá.
It is one of the largest sites with carved monuments on the Pacific coast.
Olmec-style sculptures include a possible colossal head, rock carvings and others.
The site has one of the biggest collections of Olmec-style sculpture outside of the Gulf of Mexico.
Takalik Abaj shows the first signs of Maya culture that happened by about 400 BC.
The site includes a Maya royal tomb and examples of Maya writing that are among the first from the Maya region.
Studies continue at the site; the monumental buildings and long tradition of sculpture in a variety of styles suggest the site was important.
Finds from the site indicate contact with the distant city of Teotihuacan in the Valley of Mexico.
They imply that Takalik Abaj was conquered by it or its allies.
Takalik Abaj was linked to long-distance Maya trade routes that let the city take part in a trade network that included the Guatemalan highlands and the Pacific coastal plain from Mexico to El Salvador.
Takalik Abaj was a large city with the main buildings in four main groups spread across nine terraces.
While some of these were natural, others were man-made, needing a lot of work and materials.
The site had a clever water drainage system and many stone sculptures.
Takalik Abaj at The Guatemala Times online .
Information and news in English, some by investigating archaeologists.
Site description and gallery
Currys (UK)
Currys (IRL)
Moneysavingexpert Forum re: Currys Customer Service
García Robles received the Nobel Peace Prize in 1982, together with Sweden's Alva Myrdal.
García Robles was  the driving force behind the Treaty of Tlatelolco.
This treaty established a nuclear-free zone in Latin America and the Caribbean.
Mexican Nobel  Prize winners
Mexican politicians
People from Michoacán
Ouangolodougou, Côte d'Ivoire is a small town in the northern part of Ivory Coast, a country in western Africa.
It is located in the Ferkessédougou Department.
Ouangolodougou is near the border of Côte d'Ivoire and Burkina Faso.
A Pinto horse is a spotted horse.
They are not a breed, but a coat color.
In fact, any horse breed can be a Pinto as long as they have patches of white or another color.
Pintos are often confused with Paints, a horse breed.
They look very similar.
The difference is that a Paint is a breed, and a Pinto is a coat color that can be on any breed, including Paints.
Pintos are so old that they were found in tombs in Ancient Egypt dating back to 4 B.C.  In the 16th century Cortez brought thousands to the New World.
Some of them were set free, and Native Americans caught them.
The Native Americans liked them for their toughness and their color.
Their color blended in with the environment and made a natural camouflage.
They were known to make great war horses.
Their name came from the Spanish word pintado, which means “painted”.
Pintos have pink skin, blue eyes, and white or multicolored hooves.
They can be either a white horse with colored patches, or a colored horse with white patches.
It has been said that no two Pintos are exactly alike.
Tobiano: The Tobiano is the most common.
They are white, with large colored spots that often overlap.
Overo: A colored horse with jagged white markings.
Tovero: A Tovero is a mix of Tobiano and Overo.
Stock: A Western horse, usually a Quarter Horse or a Paint
Hunter: An English horse, usually a Thoroughbred or a European Warmblood
Pleasure: Usually an Arabian, Andalusian, or a Morgan
Saddle: A gaited horse, usually a Saddlebred, Hackney, or a Tennessee Walker
Miniature: usually about 34 inches.
Miniature B: usually about 34-38 inches.
Pony: usually about 38-56 inches.
Horse: 56 inches and up.
Darrell Lee Waltrip (born February 5, 1947) is a retired American racecar driver.
Waltrip won three Monster Energy NASCAR Cup Series championships and 84 races, including the 1989 Daytona 500.
He is now part of the broadcast team for Fox Sports.
Waltrip’s younger brother, Michael Waltrip, owned and raced for his own team in NASCAR.
In June of 2011 Waltrip was given a spot in the NASCAR Hall of Fame.
He is a part of the Hall of Fame class of 2012.
The Black Forest cake, also called Schwarzwälder Kirschtorte, is an authentic German cake made up of a chocolate layer cake with cherries in the middle and whipped cream on top.
They are traditionally made with fresh Morello cherries, poached in a sugar syrup and pitted.
It is a variation of the chocolate cake, and sometimes decorated with chocolate curls.
Jeremy Charles Robert Clarkson (born 11 April 1960) is an English television host, writer who reports on cars.
He was born in Doncaster, West Riding of Yorkshire.
He is best known for presenting BBC TV show Top Gear with Richard Hammond and James May.
He is also known for controversial remarks.
Clarkson was ranked 49th on Motor Trend Magazine's Power List for 2011.
It is a list of the fifty most important figures in the automotive industry.
Shows he has appeared in
Other roles
Books he has written
Two books with the best columns from previous publications, called "The Collected Thoughts Of Clarkson" and "Never Played Golf" were issued by Top Gear Magazine, in 2003 and 2004.
People from Doncaster
Ward was a right-handed batsman who bowled right-arm medium pace.
He was born in Sydney, New South Wales.
He is the second longest-lived cricketer, behind England's Jim Hutchinson, who at the time of his death was 103 years and 344 days old.
Hypothermia is a condition when a person is so cold that the body temperature drops below normal.
Hypothermia is any body temperature lower than .
Someone with hypothermia starts shivering and cannot stop.
The person then becomes confused and acts strange.
Their words don't make sense and they may be clumsy.
Sometimes they become very tired.
If someone gets hypothermia, wrap the person in blankets and take them to the hospital.
If that's impossible, warm up the person slowly and give them a warm drink.
Mild
When hypothermia begins, a person feels cold, starts shivering and can't stop.
The person cannot do complicated things with his or her hands.
They are also unable to touch their thumb with their little finger, because their hand muscles don't work well.
Mild hypothermia is sometimes used on purpose by doctors for treating some medical problems.
It takes blood away from the skin, hands and feet, and puts it to the brain and important internal organs.
This helps when the person is bleeding from cuts or other wounds, and also helps when the patient goes into cardiac arrest.
Moderate (Middle)
The person begins shivering very strongly.
Their large muscles do not work well.
They move slowly and with difficulty, growing a little confused and walking unsteadily.
The person becomes pale, and lips, ears, fingers, and toes might become blue.
This is because the body is trying to keep the most important organs warm.
The person might feel sick in their stomach and very tired, wanting to go to sleep, anywhere.
Body temperature drops even more, but the person usually stops shivering.
They cannot talk clearly; they think slowly, and they cannot move their hands.
Sometimes a person will feel suddenly warm, as if they are getting better, but this just means they are getting worse.
They may take off warm clothes or lay down to go to sleep.
If this continues, they cannot walk or answer questions.
Their pulse becomes weaker, but the heart may beat faster.
Finally, the person dies.
Princeton Outdoor Guide to Hypothermia
eMedicine: Hypothermia
Wilderness Management of Hypothermia
Rapids are found on rivers.
Rapids are formed by one or more of the following:  constriction, obstruction, gradient, and flow rate.
For instance, when water is flowing swiftly over a rocky river bed, rapids can be formed.
Rapids are typically found in or near the mountains, due to the element of gradient.
Formally, the word "rapids" is always plural, (like "scissors" and "trousers"), but is often used in the singular when speaking of a specific rapid or when it would be grammatically awkward; e.g., "Sweet's Falls Rapids vs. Sweet's Falls Rapid).
The word "rapid" means "very fast."
Because of the splash made by the water going over rocks, rapids are also called "whitewater".
Some people enjoying whitewater canoeing or whitewater rafting as a sport.
Wáray-Wáray or Warai (commonly spelled as Waray; also Winaray or Lineyte-Samarnon) is a language spoken in the provinces of Samar, Leyte, and Biliran in the Philippines.
The Waraynon group of languages consists of Waray, Waray Sorsogon and Masbate Sorsogon.
All the Warayan languages belong to the Visayan language family and are related to Cebuano and more closely to Hiligaynon and Masbatenyo.
Waray-Waray is one of the ten officially recognized regional languages in the Philippines and used in the local government.
It is spoken throughout the islands especially in the Eastern Visayas region.
But it is also spoken in some parts of Mindanao, Masbate, Sorsogon and Metro Manila where Warays went to.
There is also a very small number of Filipinos abroad, especially in the United States, that speaks this language.
The Waray language has sixteen consonants: .
There are three main vowels: a , i , and u .
Consonants  and  were once allophone but cannot interchange, like palaron (to be lucky) [from palad, palm (because someone's luck is seen in the palm)] but not paladon and tagadiín (from where) [from diín, where] but not tagariín.
Native numbers are used for numbers one through ten.
From eleven onwards, Spanish numbers are exclusively used in Waray today, their native counterparts being almost unheard of by the majority of native speakers numbers (except for gatus for hundred and yukot for thousand).
Some, specially the old ones, are spoken alongside the Spanish counterparts.
Some common words and phrases
Can you understand Waray?:
Nakakaintindi / Nasabut ka hin Winaray? (
hin or hiton)
Good morning (noon / afternoon / evening): Maupay nga aga (udto / kulop / gab-i)
Thank you: Salamat
I love you: Hinihigugma ko ikaw or Ginhihigugma ko ikaw or Pina-ura ta ikaw
Where are you from? :
Taga diin ka?
or Taga nga-in ka?
What is your name? :
Ano it imo ngaran?
Who are you?:
Hin-o ka?
How are you? :
Kumusta ka na?
I'm fine / In God's will: Kalu-oy sa Dyos
How much is this? :
Tag pira ini?
I like this / that:  Karuyag ko ini / itun
I can't understand: Diri ako nakakaintindi or Diri ako nakakasabut
I don't know: Diri ako maaram or Ambot
What: Ano
Who: Hin-o
Where: Hain or Di-in
When (future): San-o
When (past): Kakan-o
Why: Kay-ano
How: Gin-aano?/Patiunan-o?
Yes: Oo
No: Dire / Diri
There: Adto or Didto or Ngad-to
Here: Didi or Nganhi or Din-hi
Up: Igbaw
Down: Ubos
Top: Baw-baw
Bottom: Ilarom or Sirong
Right: Tu-o
Left: Wala
Far: Harayu / Harayo
Near: Hirane / Hirani
Front or in front: Atubang or Atubangan
Night: Gab-i
Day: Adlaw
Nothing: Waray
Good: Maupay
Beautiful: Mahusay
Handsome: Gwapo
Boy: Lalaki
Girl: Babayi
Gay: Bayot
Lesbian: Lesbyana
I'm a friend of...: Sangkay ak ni...
I'm lost here: Nawawara ak didi.
Maybe: Bangin
I wish...: Kunta
Other common words
Technical terms
Gold - Bulawan
Steel - Puthaw
Car - Awto / Sarakyan / Kotchi / Sasakyan
Airplane - Edro / Eroplano
Airport - Lupadan / Landingan
Astronomical terms
Earth - Kalibutan
Moon - Bulan; Indonesian - Bulan
Sun - Adlaw
Star - Bituon Indonesian - bintang
Natural terms
Wind - Hangin; Indonesian - Angin
Fire - Kalayo
Land - Tuna; Indonesian - Tanah
Water - Lawod / Tubig
Nature - Libong
Mountain - Bukid; Indonesian - Bukit
Sea - Dagat
Ocean - Kalawdan Indonesian - Laut i.e. ka-laut-an
Island - Puro / Isla Indonesian - Pulau
Archipelago - Kapuruan; Indonesian - Kepulauan
River - Salog
Lake - Danaw; Indonesian - Danau
Parts of the house
House - Balay or Payag
Room - Kwarto or Sulod
Bedroom - Sulod-Katurugan
Kitchen - Kusina
Outdoor Kitchen - Abuhan
Living Room - Sala
Dining Room - Kaunan
Bathroom - Kubeta / Kasilyas / Karigu-an / Banyo
Stairs - Hagdan / Hagdanan
Garage - Garahe / Garahi
Roof - Atup / Atop
Members of the Family
Father - Amay / Tatay / Papa
Mother - Iroy / Nanay / Mama
Child - Anak
Son - Anak nga Lalaki
Daughter - Anak nga Babayi
Sibling - Bugto
Brother - Bugto nga lalaki
Sister - Bugto nga Babayi
Grandparent - Apoy
Grandfather - Lolo
Grandmother - Lola
Cousin - Patod
Nephew/Niece - Umangkon
Son-in-Law/Daughter-in-Law - Umagad
Brother-in-Law - Bayaw
Sister-in-Law - Hipag
Father-in-Law/Mother-in-Law - Ugangan
Oldest Child - Suhag
Youngest Child - Puto or Pudo
Fashion words
Hat - Kalo
Pants - Saruwal
Clothes - Bado / Duros
Belt - Paha
Socks - Medyas
Shoes - Sapatos
Bread - Tinapay
Rice (cooked) - Kan-on / Luto
Rice (unhusked and raw) - Bugas
Rice (still in husk) - Humay
Rice (charred) - Tukag
Viand - Sura
Coffee - Kape
Sugar - Asukar
Salt - Asin
Soy Sauce - Toyo
Vinegar - Suoy / Suka
Dog - Ayam / Iru / Ido
Cat - Uding / Misay
Rat - Yatot / Yatut
Crocodile - Buaya
Bird - Tamsi
Snake - Halas
Cow - Baka
Pig - Baboy
Goat - Kanding
Carabao - Karabaw
Fish - Isda
Crab - Masag
Shrimp - Pasayan
Lobster - Tapusok
Waray-Waray loanwords and cognates
Common Waray Waray words and its foreign and local origin
Indonesian/Malay Cognates
Mulay (English: to play)- from Indonesian mulai
Balay (English: house) - from Indonesian balai
Sarapati (English: pigeon) - from Indonesian merpati
Kapuruan (English: archipelago) - from Indonesian/Malay kepulauan
Posporo (English: match) - from Indonesian/Malay posporo
Mata (English: eyes) - from Indonesian/Malay mata
Bulan (English: moon/month) - from Indonesian/Malay bulan
Ini (English: this/these) - from Indonesian/Malay ini
Kamo (English: you [plural]) - from Indonesian/Malay kamu
Abandonada (Spanish: Abandonado/a) – abandoned
Abaniko (Spanish: Abanico) – fan
Abriha (Spanish: Abrir, Filipino: Abrihin) – to open
Abrelata (Spanish: Abrelatas) – tin-opener/can opener
Abril (Spanish: Abril) – April
Abogado (Spanish: Abogado) – lawyer, attorney
Aborido (Spanish: Aburrido) – bored (used in Tagalog as 'anxious, confused')
Akasya (Spanish: Acacia) – acacia tree
Aksidente (Spanish: Accidente) – accident
Adurnuha (Spanish: Adornar, Filipino: Adurnuhan) – to decorate
Agrabiyado (Spanish: Agraviado) – being aggrieved
Aginaldo (Spanish: Aguinaldo) – Christmas gift
Agosto (Spanish: Agosto) – August
Ahensiya (Spanish: Agencia) – agency
Ahente (Spanish: Agente) – agent
Alahas (Spanish: Alhaja) – jewel
Alambre (Spanish: Alambre) – wire
Alkansiya (Spanish: Alcancía) – piggy bank
Alpilir (Spanish: Alfiler) – pin
Alsaha (Spanish: Alzar, Filipino: Alsahin) – Ambisyoso (Spanish: Ambicioso) – ambitious
Ambisyon (Spanish: Ambición) – ambitionArbularyo (Spanish: Herbolario) - Medicine man (from "Herbo" -herb)
Arina (Spanish: Harina) – flour
Arkitekto (Spanish: Arquitecto) – architect
Armado (Spanish: Armado) – armed
Armibal (Spanish: Almíbar) – syrup
Artista (Spanish: Artista) – artist (used in Waray Waray as 'actor/actress')
Ariyos (Spanish: Arreos) – tack (used in Waray Waray as 'earrings')
Asintado (Spanish: Asentado) – settled
Asero (Spanish: Acero) – steel
Asno (Spanish: Asno) – donkey
Asoge (Spanish: Azogue) – mercury
Asosasyon (Spanish: Asociación) – association
Asukar (Spanish: Azúcar) – sugar
Asul (Spanish: Azul) – blue
Asyatiko (Spanish: Asiatico) – Asian
Intyendeha (Spanish: Atender) – to attend to
Atrasado (Spanish: Atrasado) – overdue, slow (clock), backward (used in Waray Waray as 'late')
Ayudaha (Spanish: Ayudar, Filipino: Ayudahan) – to help
Banyo/Kasilyas (Spanish: Baño) – bathroom, toilet
Baraha (Spanish: Baraja) – deck of playing cards
Baratilyo (Spanish: Baratillo) – flea market (used in Waray Waray as 'bargain sale')
Barato (Spanish: Barato) – cheap
Barbero (Spanish: Barbero) – barber
Barbula (Spanish: Válvula) – valve
Bareta (Spanish Bareta) – bar
Bagahe (Spanish: Bagaje) – baggage
Baho (Spanish : Vaho) – steam (used in Waray Waray as 'foul smell')
Bintana (Spanish: Ventana) – window
Bintilador (Spanish: Ventilador) – electric fan
Birhen (Spanish: Virgen) – virgin
Bisagra (Spanish: Bisagra) – hinge
Bisikleta (Spanish: Bicicleta) – bicycle
Bisitaha (Spanish: Visitar) – to visit
Botika/Botica/Parmasya/Farmacia - drugstore, pharmacy
Conbensido (Spanish: Convencido) - convinced
Demanda (Spanish: Demanda) – demand
Demokrasiya (Spanish: Democracia) – democracy
Demonyo (Spanish:Demonio) – demon, evil spirit
Huygo (Spanish:Juego)- game (used in Waray Waray as 'gambling'
Hugador (Spanish:Jugador)- game (used in Waray Waray as 'gambler'
Dentista (Spanish: Dentista) – dentist
Departamento (Spanish: Departamento) – department, bureau
Depensa (Spanish: Defensa) – defense
Deposito (Spanish: Depósito) – depot (fuel), deposit (money)
Desisyon (Spanish: Decisión) – decision
Diyos/a (Spanish: Dios/a) – god/goddess
Doble (Spanish: Doble) – double
Doktor/a (Spanish: Doctor/a) – doctor
Don (Spanish: Don) – Mr. (used in Waray Waray to address a rich man)
Donya (Spanish: Doña) – Mrs. (used in Waray Waray to address a rich woman)
Dos (Spanish: Dos) – two
Dose (Spanish: Doce) – twelve
Dosena (Spanish: Docena) – dozen
Drama (Spanish: Drama) – drama
Droga (Spanish: Droga) – drugs
Karsonsilyo/Carsoncillo (Spanish: Carsoncillo) – boxer shorts (used in Waray Waray as 'shorts')
Marigoso (Spanish: Amargoso) - bittermelon
Padre (Spanish: Padre) - father (used in Waray Waray as a title for a Roman Catholic priest)
Porta (Portuguese: Porta) - door
Multo (Portuguese: Morto) - ghost
Achuete (Nahuatl: Achiotl; Mexican Spanish: Achiote) – annatto seeds used to give food a reddish color
Kakao/Kakaw (Cacao) (Nahuatl: Cacahuatl) – cacao or cocoa
Sayote (Nahuatl: Chayotli; Mexican Spanish: Chayote) – a Mexican squash
Tiyangge (Nahuatl: Tianquiztli; Mexican Spanish: Tianguis) – seasonal markets
Tsokolate (Nahuatl: Xocolatl) – chocolate
Bakya (Fukien Chinese) – native wooden sandals
Bihon – Vermicelli (made of rice flour)
Bitsin (Fukien Chinese: Bi chhin) – monosodium glutamate
Jueteng (Fukien Chinese) – illegal numbers game
Lumpia (Fukien Chinese) – spring rolls
Basket – basket
Basketbol – basketball
Basketbulan - basketball court
Bilib - believe
Bilyar - billiard
Bilyaran - billiard hall
Chiki - check
Dyeepnee – jeep
Elementari – elementary
Ekonomiks - economics
Eksport – export
Ekpres - express
Erkon - air con
Greyd – grade
Groseri – grocery
Hai Skul – High School
Iskor – score
Iskrin – screen
Ispiker - speaker
Keyk – cake
Kostomer/Kustomer – customer
Kompyuter – computer
Kondisyoner - conditioner
Kontrol - control
Krim - cream
Kukis - cookies
Lider – leader
Losyon - lotion
Manedyer – manager
Masel – muscle
Makroekonomiks - macroeconomics
Maikroekonomiks - microeconomics
Isparkol - sparkle
Bana (Cebuano: Bana) - husband
Radyo Waraynon - Waraynon Internet Radio Station
Waray Museum Blog featuring Waray literature
Online Lineyte-Samarnon (Waray)-English Dictionary (also with Videos, Photos, Music, News, Local Destinations)
Waray lessons
Bansa.org Waray Dictionary
Ethnologue Report for Waray
A downloadable Waray dictionary with etymologies and Cebuano, Tagalog cognates by Andras Rajki
Waray Explained  (Online Tutorial)
Languages of the Philippines
James Ewell Brown Stuart (1833-1864) was a general in the Confederate army during the American Civil War.
He was from Virginia.
During the war, he was known for dangerous things he did while riding a horse.
He was killed at the Battle of Yellow Tavern in 1864.
Riodinidae is a family of butterflies.
They are commonly known as riodinids or metalmarks.
Metalmarks get their name from the bright, metallic (looking like metal) markings found on the wings of most species.
The family has nearly 2,000 species in it.
The metalmarks are mostly found in the Neotropical region.
Most metalmarks are small.
Their wingspan ranges from 20mm to 65mm.
Metalmarks vary greatly in wing shape, pattern, and color.
Riodinidae was formerly known as the family Nemeobiidae and as the family Erycinidae.
It was also once thought to be a subfamily of Lycaenidae.
Euselasiinae
Nemeobiinae - This subfamily is sometimes treated as a tribe.
Riodininae
Some species
Hamearis lucina - Duke of Burgundy
Apodemia mormo - Mormon Metalmark
Lasaia sula - Blue Metalmark
Melanis pixe - Red-bordered Pixie
A taxicab number is the name given by mathematicians to a sequence of special numbers: 2, 1729 etc.
A taxicab number is the smallest number that can be expressed as the sum of two positive cubes in n distinct ways.
It has nothing to do with taxis, but the name comes from a well-known conversation that took place between two famous mathematicians: Godfrey Hardy and Srinivasa Ramanujan.
The story about Godfrey Hardy’s taxi
Godfrey Hardy was a professor of mathematics at Cambridge University.
One day he went to visit a friend, the brilliant young Indian mathematician Srinivasa Ramanujan, who was ill.
Both men were mathematicians and liked to think about numbers.
When Ramanujan heard that Hardy had come in a taxi he asked him what the number of the taxi was.
Hardy said that it was just a boring number: 1729.
Ramanujan replied that 1729 was not a boring number at all: it was a very interesting one.
He explained that it was the smallest number that could be expressed by the sum of two cubes in two different ways.
This story is very famous among mathematicians.
1729 is sometimes called the “Hardy-Ramanujan number”.
Explanation of the Hardy-Ramanujan's number
When a particular number is multiplied by itself the answer is called a “square”, e.g. 3x3=9, so the number 9 is a square.
When a particular number is multiplied thrice by itself the answer is called a “cube”, e.g. 3x3x3=27, so the number 27 is a cube.
Another example of a cube is 8, because it is 2x2x2.
27+8=35, so 35 is the “sum of two cubes” (“sum” in this sense means “numbers that are added together”).
1x1x1=1;  12x12x12=1728.
So 1+1728=1729
But also:  9x9x9=729;  10x10x10=1000.
So 729+1000=1729
Known taxicab numbers
Since the famous conversation between Hardy and Ramanujan, mathematicians have tried to find other interesting numbers that are the smallest number that can be expressed by the sum of two cubes in three/four/five etc.
different ways.
These numbers are very, very big, and have been found by computers.
Bernard Frénicle de Bessy (about 1605–1675), was a French mathematician.
He wrote many papers about mathematics,  number theory and combinatorics.
The Frénicle standard form, a standard representation of magic squares, is named after him.
He solved many problems created by Fermat.
He also discovered a taxicab number and in 1693, he described all 880 essentially different normal magic squares of order 4.
Like Fermat, Frénicle was an amateur mathematician, but he wrote letters to famous people such as Descartes, Christiaan Huygens, Mersenne and also Fermat, who was his friend.
He is mainly remembered for his discoveries about number theory.
1600s births
Płońsk is a city in Central Poland in the Masovian Voivodeship.
It has a population of 23,000 and has an area of 12 km².
It is the birthplace of the Zionist leader and first Prime Minister of Israel, David Ben-Gurion.
Map of the City of Płońsk
Official website of the City of Płońsk
Frances Burney (13 June 1752 – 6 January 1840) was an English novelist, diarist and playwright.
She was also known as Fanny Burney.
After her marriage, she was known as Madame d’Arblay.
She was born in King's Lynn, England.
She was born to musician Dr Charles Burney (1726 – 1814) and Mrs Esther Sleepe Burney (1725 – 62).
She mostly taught herself.
She began writing what she called her "scribblings" when she was ten.
Her first novel, Evelina, was published in 1778.
This novel made her very famous.
Cecilia came out in 1782.
It was an even greater critical success.
Her major novels, Evelina, Cecilia, and Camilla are about a young girl.
The girls are clever and beautiful, but does not have a lot of experience.
The girl goes out into the world and grows in character.
Her books were liked by Jane Austen.
In 1786, she became Second Keeper of the Robes to Queen Charlotte.
She wrote many journals and letters.
Her journals and letters have interested historians.
In 1793, she married a French exile, General Alexandre D'Arblay.
They had a son in 1794.
His name was Alexander.
While living in France from 1802 to 1812, Burney wrote The Wanderer.
It was a novel about the French Revolution.
It was published in 1814.
Her last published work was the Memoirs of Doctor Burney (1832).
She died in London in 6 January 1840.
She was buried in Bath near her husband and son.
On 13 June 1752, Frances Burney was born in King's Lynn.
She was baptized on the 7th of July.
Her older brothers and sisters were Ester (Hetty) (1749 – 1832) and James (1750 – 1821).
Her younger brothers and sisters were Susanna Elizabeth (1755-1800), Charles (1757-1817) and Charlotte Ann (1761 – 1838).
Susanna Elizabeth became Frances Burney's close friend.
James Burney became an admiral.
He sailed with Captain James Cook on his second and third trips.
The younger Charles Burney was a scholar.
Her younger half-sister, Sarah Burney (1772 – 1844), also became a novelist.
She published five works that she wrote herself.
Esther Sleepe Burney also had two boys who died at birth.
First mother
Esther Sleepe Burney was three years older than Charles Burney.
She had her oldest daughter, Esther, with Charles before they married.
Frances Burney kept this as a "family secret".
She even said nothing about the date of her father's marriage.
Also, she did not say when his children were born in the Memoirs.
Some people have thought that she hid the dates to make everyone believe she published Evelina when 17.
Her mother suddenly became sick.
She took a trip to Bath and Bristol Hot Wells.
This is where main character in Evelina go to try to become healthy again.
However, she did not get better.
The sickness was thought to be tuberculosis.
It is also possible that it was cancer.
In 1760, her mother, Esther Sleepe Burney, died.
She was described by historians as a gentle woman of "warmth and intelligence".
It is possible that Esther Burney's French birth influenced Burney's writing.
One example is the conflicts between Madame Duval and Captain Mirvan in Evelina.
It may also have been one reason for her love of and marriage to Alexandre D'Arblay.
Fanny was very shocked and sad when she heard that her mother was dead.
Her neighbor, Mrs. Pringle, commented.
She later said, "...she never saw such affliction" and that Fanny would "take no comfort--& was almost killed with [sic] Crying".
Her father, Charles Burney, was also very unhappy.
He comforted himself with writing sad poems about his wife.
Her father was respected by many people as a musician.
He was also well-educated.
He wished to show that a musician could be a gentleman.
Frances Burney often saw many opera singers, dancers, musicians, and actors (like actors Garrick or Christopher Smart), that spoke in many kinds of languages.
She mentioned him in Evelina: "Well may Mr. Garrick be so celebrated, so universally (everywhere) admired—I had not any idea of so great a performer...every look speaks!...I am afraid you will think me mad (crazy), so I won't say any more; yet I really believe Mr. Garrick would make you mad too, if you could see him."
She also saw more of the world than most "young ladies" could.
She wrote down many rude things people said in her diaries.
Traveller Richard Twiss once embarrassed the family by talking about improper things.
He said that an immodest book, The Dictionary of Love, was very good.
After Twiss left, Burney wrote in her Diary, 'Even my gentle & candid (truthful) Father says that he has quite mistaken the Thing, & that he will never see a Table Cloth in his House again'.
Some people have said that Burney may have been shy because of her father.
People said that Mr. Burney's only fault was "obsequiousness" (too much serving to men).
Frances never openly criticized her father.
She even carefully destroyed everything bad about him.
In her Memoirs, she wrote that her father had no faults.
However, she wrote explanations and excuses for things her father thought were right.
Second mother
In October 1767, her father married a rich widow.
Her name was Elizabeth Allen.
She already had three sons.
The Burney children did not like their stepmother.
Hester, Frances's older sister, married her cousin.
His name was Charles Rosseau Burney.
He was a musician.
She married him in September 1770.
She probably did this to leave her home.
Because of this, Frances lost a sister who was like another mother.
The Burney children did a "secret war" with Mrs. Allen.
They called her "Mrs. Precious", "Madam", and "the Lady".
A letter from Frances Burney to her sister Hester said, "The excuse to be fudged up (made up, lied) for the purpose, I leave to your own ingenuity."
Although at this time Frances was 25 years old, she had to find an excuse to visit her married sister.
Even their old friend, Samuel "Daddy" Crisp, joined in with mocking Mrs. Elizabeth Allen.
Her father educated her sisters Esther and Susanna much more than Frances Burney.
When she was eight, she still had not learned the alphabet.
She was also so shy that visitors at her father's house called her the "old lady".
Some scholars think she might have had a kind of dyslexia.
Her brother used to play tricks on her by pretending to teach her to read and giving her a book upside-down.
She did not find out that it was actually upside down and tried to read it.
People said that "the little dunce" should be whipped.
However, Esther Sleepe Burney always replied that "she had no fears about Fanny".
Her sister Susanna said that Fanny has "sense, sensibility, and bashfulness (shyness)".
She also added, "I am afraid...that my sister Fanny is too reserved".
In 1763 or 1764, Samuel "Daddy" Crisp became close to the Burney family.
He helped Frances write by asking for many journal-letters from her about her family and her life.
He influenced her writing very much.
Frances Burney d'Arblay made a new kind of English novel, recording things that happened from George III's madness to what happened after the Battle of Waterloo.
She also wrote comedies that had a great influence on many writers to come.
For example, Jane Austen found both the theme and the title for Pride and Prejudice in the last chapter of Frances Burney's novel Cecilia.
William Makepeace Thackeray, the writer of Vanity Fair, was also influenced by Burney.
Her first novel, Evelina, was a new kind of fiction in English.
It was a fiction where women in society were shown in realistic, modern ways - the novel of manners. "
She showed the manners and morals of polite society with a relish (liking) for the ridiculous (funny) and a respect for the conventional (traditional)".(Norton Anthology of Literature by Women, p. 242) Burney was the first woman to make the writing of novels "respectable".
Her second novel, Cecilia, published in 1782, was an even greater critical success.
Her third novel, Camilla, was very popular; the sale was "4 times that of Evelina, & nearly double that of Cecilia".
Essays by Fanny Burney at Quotidiana.org
http://www.mytimemachine.co.uk/operation.htm  Fanny Burney's own account of the mastectomy she underwent in 1811.
Burney Centre at McGill University
http://dc37.dawsoncollege.qc.ca/burney/ The Burney Society
Valerie Patten, author biography of Frances Burney (1752-1840)
Lake Placid is a village in northern New York State.
It has a population of 2,638.
It was founded in the early 1880s to look for iron.
Today it is a ski resort.
It has hosted the Winter Olympics twice, in 1932 and 1980.
Web site of the Lake Placid/Essex County Visitors Bureau
Web site of the Lake Placid News
Lake Placid information
Lake Placid Olympic Authority
Ski areas and resorts
A grebe is a medium sized bird.
They are in the family Podicipedidae.
There are 22 species of grebe.
Genera and species
Genus Tachybaptus
Little Grebe, Tachybaptus  ruficollis
Australasian Grebe Tachybaptus novaehollandiae
Madagascar Grebe, Tachybaptus pelzelnii
Alaotra Grebe, Tachybaptus rufolavatus — probably extinct (late 1980s)
Least Grebe, Tachybaptus dominicus
Genus Podilymbus
Pied-billed Grebe, Podilymbus podiceps
Atitlán Grebe, Podilymbus gigas — extinct (1989)
Genus Rollandia
White-tufted Grebe, Rollandia rolland
Titicaca Flightless Grebe, Rollandia microptera
Genus Poliocephalus
Hoary-headed Grebe, Poliocephalus poliocephalus
New Zealand Dabchick, Poliocephalus rufopectus
Genus Podiceps
Red-necked Grebe, Podiceps grisegena
Great Crested Grebe, Podiceps cristatus
Slavonian Grebe or Horned Grebe, Podiceps auritus
Black-necked Grebe or Eared Grebe, Podiceps nigricollis
Colombian Grebe, Podiceps andinus — extinct (1977)
Great Grebe, Podiceps major
Silvery Grebe, Podiceps occipitalis
Junin Flightless Grebe, Podiceps taczanowskii
Hooded Grebe, Podiceps gallardoi
Genus Aechmophorus
Western Grebe, Aechmophorus occidentalis
Clark's Grebe, Aechmophorus clarkii
Description, color and shape
Most grebes are a medium or large size.
Some grebes, such as the Little Grebe are smaller.
All Grebes have large feet with lobed toes.
This means that each toe is separate on the foot (the opposite of this is webbed feet which is seen in ducks and geese).
Some grebes find it difficult to walk on land because their feet are so big.
They are much better at swimming and diving in water.
Grebes have narrow wings.
Some grebes find it difficult to fly.
There are two species of grebe that cannot fly at all.
This means that if grebes are in danger, they will dive under water instead of flying away like other birds do.
Grebes can have long or short bills.
If they eat insects in the water, they will have a short bills.
If they eat crustaceans (for example, crabs) they will have a long, sharp bill.
Most grebes are brown, white and red/orange.
They have many, waterproof feathers.
This means they can easily float on water and dive into water without getting cold or wet.
In spring and summer, grebes have orange crests on their heads.
This is so they can attract a mate.
Some grebes do a mating ritual.
This is when they "dance" in the water.
Grebes make their nest from plants found in the water.
The nests float on top of the water.
Baby grebes can swim when they are born.
They are usually brown and white and do not get their orange crests until they are adults.
Grebes live in freshwater (lakes or rivers).
Some species of grebe will go to saltwater (sea/ocean) when they are migrating.
This is when birds fly to live in a different place in summer or winter.
Grebes only migrate if they live in North America, Europe or Asia.
Grebes in South America, Africa and Asia do not migrate.
They are found in every continent on earth.
A Funeral Director also called a mortician or undertaker is a person who has the job of organizing a funeral.
This often includes embalming and burial or cremation of the dead, as well as the planning and arrangement of the actual funeral ceremony.
They place the body into a coffin or casket.
If people are going to come and look at the body before burial, the funeral director will have the body dressed, and made up with cosmetics to make it look better.
Mangroves are trees or shrubs that grow in salty water in hot places like the tropics.
Mangroves make a special saltwater woodland or shrubland habitat, called a mangrove swamp, mangrove forest, mangrove or mangal.
Mangroves grow on 1/3 of tropical shores.
They are also found in sub-tropical Africa, Asia, and the southwest Pacific.
Their twisted, tangled roots collect sediment.
Over time, the sediment may become islands, or extend the shoreline.
Mangroves live right in the sea, or at the sea edge.
Their seeds fall from the tree and grow roots as soon as they touch any kind of soil.
During low tide, they may fall in soil rather than water and start growing where they fall.
If the water level is high, they may be carried far away from where they fell.
Mangrove trees are often the beginning of what will one day be a small island.
As soil and other things collect in their roots, little bodies of land are formed – just the right place for other island vegetation to grow.
This is an example of seed dispersal by water.
Mangroves have special root-like structures.
They are aerial roots or pneumatophores.
These stick up out of the soil, and are covered in lenticels.
They take in oxygen through their pores.
These "breathing tubes" may reach heights of up to 30 cm, and in some species, over 3 m. Smaller roots with air passages move oxygen from the air to parts of the plant underwater.
For more information please visit a geography site https://www.kidsgeog.com  THANK YOU Mangrove
Mangrove roots give clear water to the coral reefs which often surround them.
They trap dirt and clean water by filtering land runoff and removing pollutants.
The tree also protects the shoreline (and, through this, the coral reefs) from being eroded by storm waves.
Mangrove thickets are a good place for many coral-reef fish, shrimp, and crabs to grow.
BBC account
Mangroves are a group of about 80 different salt-tolerant species of trees.
They can live along the intertidal zones of tropical and sub-tropical coastlines.
Their roots stand the ebb and flow of tides.
The roots slow the flow of the tidal waters.
This lets sediment settle and build up as nutrient-rich mud.
The habitat is a valuable shelter and breeding site for fish.
It stabilises coastlines, and reduces erosion from storm surges and tsunamis.
The great crested grebe is a water bird.
It is a member of the grebe family.
Its scientific name is Podiceps cristatus.
The great crested grebe is a medium sized bird.
It is 46–51 cm long.
Its wingspan (both wings open) is 59–73 cm long.
The bird is white, brown and black, and it has orange crest feathers on its head.
It has a long, sharp pink bill.
Baby great crested grebe have black and white stripes on their heads.
Habitat and behaviour
The great crested grebe is found in Europe, Asia, Africa and Australia.
It is the biggest grebe in Europe.
It lives in freshwater lakes.
It eats crustaceans (for example, crabs), insects and small frogs.
It dives into the water to find food.
The bird has an interesting mating ritual.
This means two birds (male and female) do a "dance" in the water before they mate.
Grebes dance every time the pair meets, and the dance varies according to the circumstance.
Returning to the nest is different from meeting out on the water, for instance.
Most dances end in a bout of head-shaking.
The great crested grebe makes a nest from plants.
The nest floats on top of the water.
A pair of grebes will usually have two eggs.
When the babies are born, they cannot swim.
Their parents teach them to swim and dive.
Sometimes the babies will sit on their parents backs while the parents swim in the water.
The bird nearly became extinct in the United Kingdom in the 19th century.
This is because people wanted to use their orange head feathers.
People wanted to put the feathers on their hats and clothes.
The RSPB (Royal Society for the Protection of Birds) stopped this.
There are now many great crested grebe in the United Kingdom, where their conservation status is green ("least concern").
The swift is a bird in the family Apodidae.
It is in the order Apodiformes with treeswifts and hummingbirds.
The swift is very good at flying.
It spends all of its time in the air.
The scientific name for the swift (apus) comes from the Ancient Greek word απους, apous which means "without feet".
This is because swifts have very small, weak feet.
Swifts use their feet to hold on to vertical places (for example, the wall of a house, or a cliff).
Swifts do not want to land on the ground.
It is often thought that if they land on ground, they cannot fly up again, but that is not true.
They can take off but with difficulty.
Swifts are small birds.
They can fly very well and very fast.
Some swifts can fly at 514m per second.
If a swift needs to fly very fast, it can fly at 60m per second for a short amount of time.
When catching insects, they fly in a series of swoops, changing direction rapidly as they pursue the prey.
Swifts have long, curved wings.
The wings are in the shape of a sickle or boomerang.
They have a forked tail.
This means it looks like a V shape.
Swifts can be seen all over the world.
They like to live in warmer places and they migrate every year.
For example, Swifts fly to Europe in the spring and summer.
When it gets cold at the start of autumn, the Swifts fly to Africa where it is warmer.
Nests
Swifts make their nests in a corner between two walls.
For example, near the roof of a house, or in an area between rocks in a cave.
They use mud and saliva (spit) to make a cup-shaped nest.
There are some swifts which only use saliva to make their nests.
These swifts are in the genus Aerodramus.
In Asia, people take the nests and use them to make bird's nest soup.
This soup is very popular in China.
Wangaratta is a city in the northeast of Victoria, Australia.
About 19,000 people live there.
It is about  from Melbourne along the Hume Highway.
The city of Benalla   is to the south west, and Albury and Wodonga  to the north east.
The Ovens and King Rivers which flow from the Victorian Alps meet at Wangaratta.
It is in the local government area of the Rural City of Wangaratta.
Gold was found in the area during the 1850s.
A Post Office opened on 1 February 1843, as Ovens, and moved to the town and was renamed Wangaratta in 1854.
The Ovens office, and the Kilmore office which opened the same day, were the fifth and sixth to open in the Port Phillip District (Victoria).
They were also the first two inland offices.
Chiltern is a town in the north east of Victoria, Australia.
It is between Wangaratta and Wodonga, in the Shire of Indigo.
In 2006 there were 1063 people living in Chiltern.
The town is close to the Chiltern-Mt Pilot National Park.
Chiltern was once on the main road between Melbourne and Sydney but is now by-passed by the Hume Freeway a few kilometres to the east.
The area of Chiltern was on the Wahgunyah cattle run and was called Black Dog Creek.
The township was named after the Chiltern Hills in England.
It was surveyed in 1853 but not started until gold was found in 1858—59 during the great Victorian Gold Rush period.
The Post Office opened on September 1, 1859.
Many of Chiltern's old buildings are protected by the National Trust.
In 1859, many shop-keepers and miners from around Beechworth and the Ovens Valley followed the gold rush and moved into Chiltern.
A press release, news release, media release, or press statement is a written or recorded communication for news reporters.
Its purpose is to let them know about something that is news.
These are mailed, faxed, or e-mailed to editors at newspapers, magazines, radio stations, television stations, and television networks.
There are companies whose job is to send out this information.
The use of a press release is common in public relations.
People use this to get the media to take notice of them, or get publicity for a product, or event that they might be holding.
A press release gives reporters the basic information they need to write a news story.
Press releases can announce a range of news items such as: events, promotions, awards, new products and services, sales and other financial data, accomplishments, etc.
A press statement is information given to reporters.
This is an official statement or account of a news story that is specially written for newspapers and other news media for them to make known to the public.
"Alice" is an alternative rock song written and performed by Canadian singer-songwriter Avril Lavigne for the soundtrack to the 2010 movie Alice in Wonderland, entitled Almost Alice.
The song is a mid-tempo ballad sung from the perspective of the film's lead character, Alice.
According to Lavigne, she wrote the song after asking Disney executives and director Tim Burton for a role on the soundtrack.
The song was produced by Butch Walker and mixed by Lavigne's former husband Deryck Whibley.
While designing clothes inspired by Alice in Wonderland for her Abbey Dawn line, Lavigne told Disney executives she could write a song for the film's soundtrack.
Director Tim Burton agreed, and Lavigne "wrote the song immediately" on her piano.
Lavigne described the song as "a little darker" and confirmed the lyrics, "trippin' out, spinnin' around, I'm underground, I fell down."
2010 songs
In 1912, the Sons and Daughters of Utah Pioneers ordered a custom made copy of the newly adopted state flag to be showed off to the battleship USS Utah, which was commissioned on August 31, 1911.
When the flag came, the group found out that the coat of arms on the flag was in full color instead of white, and the manufacturer had added a gold ring around the shield.
Rather than have the flag remade, the Utah legislature changed the law to match the battleship flag, and the flag was showed off to the USS Utah.
A bald eagle, the national bird of the United States represents the safety of America.
The arrows in the talons of the eagle represent courage in war.
The sego lily, the Utah state flower, represents peace.
The state motto "industry" represents progress, hard work, and community as does the emblem of the beehive, which is also a traditional Mormon symbol.
Crossed Union flags show Utah's support and commitment to the United States.
The name, Utah, appears underneath the beehive.
The date 1847 represents the year Brigham Young led the first Mormons into the state.
The year listed below that, 1896, represents the year that Utah was admitted to the Union.
The gold circle around the state seal represents eternal order.
The shield underneath the bald eagle represents common defense (military).