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These
are the seven bones of the neck, called the cervical vertebra. The top
bone, seen on the right of this picture, the atlas, is where the head attaches to the neck. The second bone is
the axis, upon which the head and atlas rotate. The vertebra
are numbered from one to seven from the atlas down, and are referred
to as C1, C2, C3, etc. (Source:
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To mathematicians, though, Königsburg is best known because of a puzzle associated with its seven bridges over the Pregel River, which were located roughly as illustrated on the left. Its citizens pondered for a long time whether it was possible to devise a walk about the city in such a way that you cross all seven bridges once and only once. |
In a 1736 paper which arguably began the field of topology, the great Swiss mathematician Leonhard Euler (1707-1783) proved that this was impossible. In fact Euler gives a criterion which allows one to quickly determine whether there is a solution for any similar problem with any number of bridges connecting any number of landmasses.
Euler first noted that the problem is not changed if we replace the landmasses by vertices (red dots in the diagram) and the bridges by arcs connecting the vertices. We call the resulting assemblage of points and arcs a graph and define the degree of a vertex to be the number of arcs that lead to/from it. Euler proved:
Theorem There exists a (at least one) path on a graph which travels along each arc exactly once if and only if the graph has at most two points of odd degree.
Such a path on a graph, if it exists, is now called an Euler path in his honour. The Königsburg example has three vertices of degree three and one of degree five, so it has no Euler path and the original puzzle has no solution.
The key to the proof of (one direction of) Euler's result is the realization that if a vertex is not the initial or final vertex of a path and each bridge is only used once, then the number of arcs that are traversed leading to/from that vertex must be even (each time you go through a vertex, you use one arc to get there and another to leave). This also shows that if there are two vertices of odd degree, one must be the initial vertex of the Euler path and the other the final vertex. Incidentally, notice that the number of vertices of odd degree in any graph must be even since the sum of all the degrees is double the number of paths. (In the Königsburg example, there are 5 vertices, the sum of whose degrees is 14, which is double the number of the 7 paths.)
The above explanation is largely taken from the website of the Department of Mathematics at the National University of Ireland, Maynooth.
Seven Bridges Road
Most often recognized as a highly-harmonized Eagles song (video here), actually written by the great American songwriter and troubadour Steve Young and also covered by Joan Baez, Rita Coolidge, Iain Mathews and Dolly Parton. It is also, apparently, the name of an actual road in Duluth, Minnesota, four miles long, which actually includes nine bridges. But it's still called the Seven Bridges Road. You can read about it's history here.
The Seven Colors of the Rainbow
Isaac Newton recorded the seven colors of the rainbow in his experiments with optics. In reality the colors blend gradually into one another. Newton's seven are:
- Red
- Orange
- Yellow
- Green
- Blue
- Indigo
- Violet
The most common mnemonic to remember these is "ROY G BIV."
The Seven Crewmembers of Challenger 7
The worst disaster in the U. S. space program. Almost anyone can tell you where they were on January 28, 1986. Here is a picture of the Challenger 7 crew:
Ellison Onizuka (Mission Specialist), Christa McAuliffe (Civilian), Gregory Jarvis (Payload Specialist), Judy Resnik (Mission Specialist), Michael J. Smith (Pilot), Francis "Dick" Scobee (Spacecraft Commander), Ronald McNair (Mission Specialist)
One of my students wrote me this email (in 2001) with her memory of Challenger 7:
... I was in fourth grade. I remember a teacher rushing to turn off the TV when it exploded. We didn't think anything wrong. We just thought it was a cool firework at first. But we noticed things were wrong because the teachers looked so scared and some had tears in their eyes. I remember calling 411 a few days later for information on how to get in contact with NASA. She gave me a number and I called. Whoever I talked to thought it was so cute that I was calling. She gave me the address and I wrote them. I even send a picture of myself. Three months later, they send me a picture of the crew and information about space camp. Till this day, I still have that picture. My parents thought I was to young to go to space camp so they never followed up on that. I would still like to work for NASA. ... I was looking at that picture a few days ago. I even found the video tape where I recorded everything when the Discovery shuttle went up. I feel so old now ...
The Chicago Seven
One of the most unusual courtroom spectacles in American history, the 1969-70 trial of seven radicals accused of conspiring to incite a riot at the 1968 Democratic National Convention in Chicago. They were:
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Abbie Hoffman, David Dellinger,
Jerry Rubin, Tom Hayden, |
Originally the Chicago Eight, Bobby Seale's trial was severed from the others. Read all about the incidents that lead up to their arrest, their laywers Leonard Weinglass and William Kunstler, Judge Julius Hoffman and other characters here.
The Seven Astronauts of Columbia (STS-107)
At 9:00am EST, February 1, 2003, 39 miles high and 16 minutes from home, the space shuttle Columbia disintegrated over Texas during reentry. There were no survivors.
Seated (from left) are Rick D. Husband (left), mission commander; Kalpana Chawla, mission specialist; and William C. McCool, pilot. Standing are (from the left) astronauts David M. Brown, Laurel B. Clark, and Michael P. Anderson, all mission specialists; and Ilan Ramon, payload specialist representing the Israeli Space Agency.
The Seven Continents of Earth
Here are the seven continents, with their approximate land area in sq. kilometers:
- Africa (30,065,000)
- Antarctica (13,209,000)
- Asia (44,579,000)
- Australia (7,687,000)
- Europe (9,938,000)
- North America (24,256,000)
- South America (17,819,000)
The Seven Days of the Week
A lot of information about the days of the week and their names in different languages can be found at http://webexhibits.org/calendars/: "Most Latin-based languages connect each day of the week with one of the seven "planets" of the ancient times..." The day of the week in English, its name in Italian, and the corresponding "planet" are given below:
- Sunday - Domenica - the sun
- Monday - Lunedi - the moon
- Tuesday - Martedi - Mars
- Wednesday - Mercoledi - Mercury
- Thursday - Giovedi - Jupiter
- Friday - Venerdi - Venus
- Saturday - Sabato - Saturn
English has retained the original planets in the names for Saturday, Sunday, and Monday. For the four other days, however, the names of Anglo-Saxon or Nordic gods have replaced the Roman gods that gave name to the planets. Thus, Tuesday is named after Tiw, Wednesday is named after Woden, Thursday is named after Thor, and Friday is named after Freya. (from webexibits.org).
The Seven Deadly Sins
- Pride
- Greed (avarice)
- Envy
- Anger (wrath)
- Lust
- Gluttony
- Sloth
The Seven Denominations of U.S. Currency
The seven denominations in circulation, with their portraits, are:
- $1 - George Washington
- $2 - Thomas Jefferson
- $5 - Abraham Lincoln
- $10 - Alexander Hamilton
- $20 - Andrew Jackson
- $50 - Ulysses S. Grant
- $100 - Benjamin Franklin
The Bureau of Engraving and Printing has some good pictures here, and the Department of the Treasury provides the answers to some currency FAQs here.
The Seven Dwarfs
From the 1937 Disney animated movie Snow White and the Seven Dwarfs:
- Sleepy
- Sneezy
- Dopey
- Bashful
- Happy
- Grumpy
- Doc
The House of the Seven Gables
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The House of
the Seven Gables in Salem, Massachusetts is also known as the Turner-Ingersoll
Mansion. Built in 1668, this is the oldest surviving 17th century wooden
mansion in New England (and does have a secret staircase). It was this
house that inspired author Nathaniel Hawthorne, who was born nearby, to
write his famous novel of the same name.Photo: Daniel Goodwin
As I was going to St. Ives ...
St Ives is a pleasant little English market town on the River Great Ouse, just under 15 miles from Cambridge. In the 14th century, the primitive English looms proved uncompetitive compared with the newer Flemish ones, and its weekly fair began to be replaced by a weekly market, which became known for its woad, old clothes and eels, before developing into an important sheep, cattle and horse market. Hence the old riddle:
As I was going to St Ives
I met a man with seven wives.
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits;
Kits, cats, sacks and wives -
How many were going to St Ives?Answer: If you take the last two lines literally, then the answer is 7 + (7)2 + (7)3 + (7)4 = 2,800 kits, cats, sacks, and wives. Other interpretations conclude the answer is 2,801 (add the man), 2,802 (the man and me), or even just 1 (only I was going to St. Ives – the man and his gaggle were going in the opposite direction).
The Seven Heavenly Orbs
The seven "planets" or heavenly orbs of ancient times are the seven celestial bodies of our solar system visible from earth with the naked eye. Here they are listed with their mass in Kilograms (the mass of the Earth is 5.976e+24 Kg).
- The Sun - 1.989e+30
- The Moon - 7.349e+22
- Mercury - 3.303e+23
- Venus - 4.869e+24
- Mars - 6.421e+23
- Jupiter - 1.900e+27
- Saturn - 5.688e+26
The notation, for the non-engineer, is "e" or "exponential" notation – a computer variant of scientific notation, where the mass of the Earth can be expressed as:
5.976e+24 Kg
= 5.967 x 1024 Kg
= 5,976,000,000,000,000,000,000,000 Kg
= 13,147,200,000,000,000,000,000,000 lb
= 53 septillion Whoppers®
The Seven Heavenly Virtues
- Faith
- Hope
- Charity
- Fortitude
- Justice
- Temperance
- Prudence
The Seven Hills of Rome
Legend says Rome was founded in 753 BC by twin boys, Romulus and Remus, abandoned by their parents and taken into the care of a she-wolf. Archaeologists believe that the city of Rome began as a series of farmsteads on a group of hills overlooking the Tiber River. The hills are:
- Palatine
- Aventine
- Capitoline
- Quarinal
- Viminal
- Esquiline
- Caelian
View of Rome from the Palatime Hill
The Seven Last Things Jesus Said
Johnny Hart, the B.C. cartoonist, was criticized for his April 15, 2001 comic strip, which you can view here. Without taking sides, here are, according to the King James New Testament, are the seven last things Jesus said:
- "Father, forgive them, for they know not what they do."
- "Truly, I say to you, today you will be with me in paradise."
- "Woman, behold your son. Son, behold your mother."
- "My God, my God, why have you forsaken me?"
- "I thirst."
- "It is finished."
- "Father, into your hands I commend my spirit."
In fact, the Bible seems curiously full of references to the number seven, from the seven days of creation to a plethora of sevens in Revelations. According to student Kenneth Cochran:
The Book of Revelation mentions several 'sevens'. There were seven letters to the seven original churches of the Christian faith. There was a book with seven seals. Seven trumpets and at the sounding of each trumpet a disaster swept the earth. Seven vials that when their contents was poured out created seven plagues. Seven thunders. A hideous beast with seven heads. The reign of the Antichrist is prophesied to be seven years long.
I leave it to you to wonder why the number seven figures so prominently in biblical verse.
The Seven Layers of the OSI Network Model
The Open Systems Interconnect (OSI) Reference Model published in 1984, was designed to provide a simplified, standardized system for the design and implementation of multivendor networks. The seven layers are:
- Physical
- Data Link
- Network
- Transport
- Session
- Presentation
- Application
A brief description of each can be found here.
The Seven Levels of Biological Taxonomy
There are at least 5 million species of organisms on Earth. To distinguish them, each is given a scientific name and located in a 7-level taxonomy that shows the relationship among these organisms based on similarity of characteristics. Here are the seven levels with the taxonomy for Homo sapiens – one of the 5 million species – as an example:
- Kingdom: Animalia
- Phylum: Chordata
- Class: Mamalia
- Order: Primates
- Family: Hominidae
- Genus: Homo
- Species: Sapiens
A nice, brief description of taxonomy is available here.
The Seven Liberal Arts and Sciences
The division of knowledge and learning into the seven liberal arts and sciences is a taxonomy formalized in the Middle Ages. offered a canonical way of depicting the realms of higher learning. The Liberal Arts were divided into the Trivium ("the three roads") and the Quadrivium ("the four roads"). Philosophy was seen as the discipline that tied these fields of knowledge together, and is depicted in the illustration below nurturing the seven liberal arts.
The Trivium:
The Quadrivium:
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For more information, take an informative "tour" in pictures of the seven liberal arts here.
The Magnificent Seven
The 1960 movie directed by John Sturges, based on Akira Kurosawa's classic Shichinin no samurai (The Seven Samurai). Here are the Magnificent Seven, with quotes from the movie so trite one wonders how it could be viewed, much less remembered:
- Yul Brynner (Chris Adams): "The old man was right. Only the farmers won. We lost. We always lose."
- Horst Buchholz (Chico): "But who made us the way we are, huh? Men with guns. Men like Calvera, and men like you... and now me."
- Steve McQueen (Vin): "We deal in lead, my friend."
- Charles Bronson (Bernardo O'Reilly): "Don't you ever say that again about your fathers, because they are not cowards. You think I am brave because I carry a gun; well, your fathers are much braver because they carry responsibility, for you, your brothers, your sisters, and your mothers. And this responsibility is like a big rock that weighs a ton. It bends and it twists them until finally it buries them under the ground. And there's nobody says they have to do this. They do it because they love you, and because they want to. I have never had this kind of courage. Running a farm, working like a mule every day with no guarantee anything will ever come of it. This is bravery."
- Robert Vaughn (Lee): "Yes. The final supreme idiocy. Coming here to hide. The deserter hiding out in the middle of a battlefield."
- James Coburn (Britt): "Nobody throws me my own guns and says run. Nobody."
- Brad Dexter (Harry Luck): ?
The Seven Mile Bridge
The Seven Mile Bridge carries US Rt. 1 from Key Vaca to the Sunshine Keys in the Florida Keys. One of the world's longest segmented overpasses, it was completed in 1982. To commemorate this major architectural feat, the city of Marathon hosts the annual Seven Mile Bridge Race. Every April, you can run with 1,500 others across this span while enjoying free beer and a famed panoramic view of the blue-green waters of the Gulf of Mexico and the Atlantic Ocean embracing.
Running parallel to this modern overpass is American magnate Henry Flagler's final installment of the Overseas Railway, the Old Seven Mile Bridge, finished in 1912 and destroyed during the Labor Day Hurricane of 1935.
The Seven Notes of the Scale
There are seven musical notes in an octave in the Western, diatonic, scale. This statement just scratches the surface of the very complex topic of music theory. The degrees of the scale, which are the notes considered relative to the tonic of the musical piece being played, or within the key of that piece, as opposed to the notes referred to by their absolute frequencies, are named as follows:
- Do (tonic)
- Re (supertonic)
- Mi (mediant)
- Fa (subdominant)
- So (dominant)
- La (submediant)
- Si (subtonic)
Musical notes each have a frequency, related to each other by integer ratios called harmonics. The absolute frequencies of the notes of the scale starting at middle C in today's current standard "concert pitch" are (in Hz):
The Seven Primary Mental Abilities
Louis Leon Thurston ((1887-1955) has been described as a "Renaissance man turned psychometrician". He was among the first to postulate that intelligence was not a single quality, but composed of separate abilities, each individually measurable. His seven Primary Mental Abilities (PMAs) are:
- Reasoning
- Associative Memory
- Computational Ability
- Verbal Comprehension
- Perceptual Speed
- Word Fluency
- Spatial Visualization
You can read more about Thurstone here. To explore the seventh PMA – spatial visualization – try this web site.
The Seven Principles of Kwanza
The official Kwanzaa web site explains that: "Kwanzaa was created to introduce and reinforce seven basic values of African culture which contribute to building and reinforcing family, community and culture among African American people as well as Africans throughout the world African community. These values are called the Nguzo Saba which in Swahili means the Seven Principles." Here are the Nguzo Saba:
- Umoja (Unity)
To strive for and maintain unity in the family, community, nation and race.- Kujichagulia (Self-Determination)
To define ourselves, name ourselves, create for ourselves and speak for ourselves.- Ujima (Collective Work and Responsibility)
To build and maintain our community together and make our brother's and sister's problems our problems and to solve them together.- Ujamaa (Cooperative Economics)
To build and maintain our own stores, shops and other businesses and to profit from them together.- Nia (Purpose)
To make our collective vocation the building and developing of our community in order to restore our people to their traditional greatness.- Kuumba (Creativity)
To do always as much as we can, in the way we can, in order to leave our community more beautiful and beneficial than we inherited it.- Imani (Faith)
To believe with all our heart in our people, our parents, our teachers, our leaders and the righteousness and victory of our struggle.
The Seven Seas
The term "The Seven Seas" refers to all the waters of Earth. Although there are many "seas" (Caspian, Black, Red, Dead, Ural, etc.), the term is usually taken to mean the great oceans:
- North Atlantic Ocean
- South Atlantic Ocean
- North Pacific Ocean
- South Pacific Ocean
- Arctic Ocean
- Antarctic (Southern) Ocean
- Indian Ocean
The Seven Sisters (The Pleiades)
The most famous star cluster on the sky. The Pleiades can be seen without binoculars from even the depths of a light-polluted city. Also known as the Seven Sisters and M45, the Pleiades is one of the brightest and closest open clusters. The Pleiades contains over 3000 stars, is about 400 light years away, and only 13 light years across. Quite evident in the above photograph are the blue reflection nebulae that surround the bright cluster stars. Low mass, faint, brown dwarfs have recently been found in the Pleiades.
The "Seven Sisters"
The nickname applied to seven distinguished women's colleges, which came about came about when the schools self-organized in 1927 in order to promote private, independent women's colleges and the premise of "separate but equal" liberal arts education for women.
The Seven Sisters Islands of the St. Johns River
On the eastern bank of Florida's St. Johns River, south of Palatka between Buffalo Bluff and the abandoned Cross-Florida Barge Canal, are the Seven Sisters Islands.
The Seven Stars of the Big Dipper
The "Big Dipper" is one of the most recognizable star formations, at least in the northern hemisphere. It is part of the constellation Ursa Major (The Great Bear). The two stars on the "pouring side" of the dipper point to Polaris, the North Star. The seven stars that make up the Big Dipper are:
- Dubhe
- Merak
- Phecda
- Megrez
- Alioth
- Mizar
- Alkaid
The Seven Steps of the Research Project
Not quite as renown, perhaps, as the other "sevens," this one is nonetheless quite useful in organizing your research. The seven steps are:
- Identify and develop your topic
- Find background information
- Use catalogs to find books
- Use indexes to find periodical articles
- Find Internet, audio, and visual resources
- Evaluate what you find
- Cite what you find using a standard format
Much more detail and useful information about each step are available here, as are very good links to current MLA and APA standards, and an excellent bibliography.
The Seven Summits
There are seven continents, and therefore seven summits – the seven highest mountains, one on each continent. There is, unfortunately, some disagreement on the seven, because the highest point in Australia (Mount Kosciusko) is not the highest point in the broader continent Australasia (which includes Indonesia, Oceana, etc.). Here is the list of the "seven summits" and their altitudes:
| Mountain | Feet | Meters | Location |
|---|---|---|---|
| Everest | 29,029 | 8,848 | Nepal/Tibet, Asia |
| Aconcagua | 22,840 | 6,962 | Argentina, South America |
| Denali (Mount McKinley) | 20,320 | 6,195 | Alaska, North America |
| Kilimanjaro | 19,339 | 5,963 | Tanzania, Africa |
| Elbrus | 18,481 | 5,633 | Russia, Europe |
| Vinson Massif | 16,067 | 4,897 | Antarctica |
| Carstensz Pyramid | 16,023 | 4,884 | Indonesia, Australasia |
| Mount Kosciusko | 7,310 | 2,228 | Australia |
If you have climbed all seven (or eight), you are quite an accomplished mountaineer. The list of those that have is available here.
7 UP®
The "uncola," it's been around since 1929, invented by C. L. Grigg. He named it, but no one knows why. Maybe it has seven flavors. Maybe six plus carbonation. You can check out their web site for some more speculation.
The Seven Words You Can Never Say on Television
It finally took the U.S. Supreme Court to decide that George Carlin's monologue was "speech" and therefore protected under the First Amendment. You can read Justice Steven's majority opinion, the monologue in its entirety, and even the dreaded "seven words" by following the link below. This is part of Carlin's web site, and I'm not responsible for anything there – although I would like to be. So, if you can take it, click here (but don't say you weren't warned!).
The Seven Wonders of the Ancient World
Lists vary, but here is a common one. Unfortunately, only the Great Pyramid of Giza still stands. I guess those pharaohs knew what they were doing.
The Seven Year's War
The seven years war (1756-1763) was mainly due to mercantilism problems between the British colonials, and the French. Along with trading problems, the British had over thirty times the amount of colonists than the French, and their need to expand pushed into the Ohio Valley, controlled by France. The war is also known as the French and Indian war. (See the excellent Military Heritage website for more.)
| Updated: 11.25.2008 |