Venn diagram

A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves circles, each representing a set; the points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S. This lends to read visualizations. In Venn diagrams the curves are overlapped in every possible way, showing all possible relations between the sets, they are thus a special case of Euler diagrams, which do not show all relations. Venn diagrams were conceived around 1880 by John Venn, they are used to teach elementary set theory, as well as illustrate simple set relationships in probability, statistics and computer science. A Venn diagram in which the area of each shape is proportional to the number of elements it contains is called an area-proportional or scaled Venn diagram.

This example involves A and B, represented here as coloured circles. The orange circle, set A, represents all living creatures; the blue circle, set B, represents the living creatures. Each separate type of creature can be imagined as a point somewhere in the diagram. Living creatures that both can fly and have two legs—for example, parrots—are in both sets, so they correspond to points in the region where the blue and orange circles overlap, it is important to note that this overlapping region would only contain those elements that are members of both set A and are members of set B Humans and penguins are bipedal, so are in the orange circle, but since they cannot fly they appear in the left part of the orange circle, where it does not overlap with the blue circle. Mosquitoes have six legs, fly, so the point for mosquitoes is in the part of the blue circle that does not overlap with the orange one. Creatures that are not two-legged and cannot fly would all be represented by points outside both circles.

The combined region of sets A and B is called the union of A and B, denoted by A ∪ B. The union in this case contains all living creatures that can fly; the region in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B. For example, the intersection of the two sets is not empty, because there are points that represent creatures that are in both the orange and blue circles. Venn diagrams were introduced in 1880 by John Venn in a paper entitled "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings" in the Philosophical Magazine and Journal of Science, about the different ways to represent propositions by diagrams; the use of these types of diagrams in formal logic, according to Frank Ruskey and Mark Weston, is "not an easy history to trace, but it is certain that the diagrams that are popularly associated with Venn, in fact, originated much earlier. They are rightly associated with Venn, because he comprehensively surveyed and formalized their usage, was the first to generalize them".

Venn himself did not use the term "Venn diagram" and referred to his invention as "Eulerian Circles". For example, in the opening sentence of his 1880 article Venn writes, "Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that called'Eulerian circles,' has met with any general acceptance..." Lewis Carroll includes "Venn's Method of Diagrams" as well as "Euler's Method of Diagrams" in an "Appendix, Addressed to Teachers" of his book Symbolic Logic. The term "Venn diagram" was used by Clarence Irving Lewis in 1918, in his book A Survey of Symbolic Logic. Venn diagrams are similar to Euler diagrams, which were invented by Leonhard Euler in the 18th century. M. E. Baron has noted that Leibniz in the 17th century produced similar diagrams before Euler, but much of it was unpublished.

She observes earlier Euler-like diagrams by Ramon Llull in the 13th Century. In the 20th century, Venn diagrams were further developed. D. W. Henderson showed in 1963 that the existence of an n-Venn diagram with n-fold rotational symmetry implied that n was a prime number, he showed that such symmetric Venn diagrams exist when n is five or seven. In 2002 Peter Hamburger found symmetric Venn diagrams for n = 11 and in 2003, Griggs and Savage showed that symmetric Venn diagrams exist for all other primes, thus rotationally symmetric Venn diagrams exist. Venn diagrams and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s. Since they have been adopted in the curriculum of other fields such as reading. A Venn diagram is constructed with a collection of simple closed curves drawn in a plane. According to Lewis, the "principle of these diagrams is that classes be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram.

That is, the diagram leaves room for any possible relation of

Cascade Aerospace

Cascade Aerospace Inc. of Abbotsford, British Columbia, Canada is a specialty aerospace and defence contractor, focused on providing long-term integrated aircraft support programs for Original Equipment Manufacturers, military and commercial customers. Cascade Aerospace is a member of the Aerospace Industries Association of Canada. Cascade Aerospace was a division of Conair Group, however in 2012 Cascade was acquired by the IMP Group of Halifax, Nova Scotia. Cascade Aerospace is headquartered in a 21 000 m2 facility at the Abbotsford International Airport, in Abbotsford, British Columbia, Canada; the facility was built in 2000 and is designed and equipped to accommodate eight narrow-body aircraft. Cascade has a satellite operation in Trenton, Ontario on the Canadian Forces Base. Cascade Aerospace Inc. began as an aircraft repair station, founded by Barry Marsden, who received his pilot's license at age 17. Marsden's enthusiasm for aviation led him to co-found the Conair Group, a specialty aviation services firm, in 1969.

Conair's initial focus was aerial forest fire control. The experience acquired in developing specialty aviation products and operating and maintaining a fleet of 90 aircraft gave Conair the expertise required to offer third-party maintenance and modifications; that expertise inspired a more expansive vision. By 1993, Marsden–forward thinking about aviation–envisioned a new enterprise dedicated to providing third-party maintenance; that became a reality when Conair moved into a new, state-of-the-art, 21 000 m2 facility in December 2000. In spring 2001, the third-party maintenance division became a separate company with a new name, Cascade Aerospace. Cascade's leadership team continued to diversify the company, entering into the military realm in 2005 when the company received its first contract with Canada's Department of National Defence for the total fleet management of Canada's fleet of Lockheed C-130 Hercules tactical airlift aircraft. Cascade offers its services and products to aircraft operators worldwide, is partnered with other global aerospace OEMs.

In 2010, Cascade received the contract for in-service support contract for the Royal Canadian Air Force's new CC-130J Super Hercules. In 2013, Cascade received a contract worth up to CA$225 million for long-term maintenance services on the planes; the contract is for work on Canada's CC-130H Hercules fleet's avionics system This newest contract bundles several smaller ones under a broader framework, making Cascade the prime service provider for various elements of the aircraft's avionics systems. These elements include program management as well as engineering, maintenance and technical information support. Lockheed Martin C-130, L-382 and L-100 Hercules and C-130J Super Hercules Boeing 737 and Boeing 757 Bombardier Q400, Dash 8 series Bombardier CRJ 100/200 regional aircraft Canadair CL-215 and CL-215T water scooper aircraft Bombardier Aerospace COM DEV International CMC Electronics Héroux-Devtek MacDonald and Associates Spar Aerospace Viking Air Cascade Aerospace Inc. company web site Abbotsford News - Canadian Prime Minister, Stephen Harper, speaks at Cascade Aerospace IMP Group Finalizes Acquisition of Cascade Aerospace Maintenance contract for military Hercules planes goes to BC company

1971 Dixie 500

The 1971 Dixie 500 was a NASCAR Winston Cup Series racing event that took place on August 1, 1971, at Atlanta International Raceway in Hampton, Georgia. Only manual transmission vehicles were allowed to participate in this race. Atlanta International Raceway is one of ten current intermediate tracks to hold NASCAR races. However, at the time, only Charlotte and New Hampshire were built; the layout at Atlanta International Speedway at the time was a four-turn traditional oval track, 1.54 miles long. The track's turns are banked at twenty-four degrees, while the front stretch, the location of the finish line, the back stretch are banked at five. Elmo Langley received the last-place finish due to an engine issue on lap 36 of 328, while Richard Petty defeated Bobby Allison by 2 car lengths in front of 22500 live spectators. Five cautions slowed the race for 48 laps. Buddy Baker qualified for the pole position with a speed of 155.796 miles per hour, while the average racing speed was 129.061 miles per hour.

Dave Marcis had problems with his vehicle's suspension on lap 38 while Raymond Williams' vehicle had a faulty transmission on lap 40. Dub Simpson blew his vehicle's engine on lap 60. Ed Negre wrecked his vehicle's transmission on lap 62. Coo Coo Marlin would over-exhaust his engine on lap 82 while Charlie Roberts did the same thing on lap 90; the suspension on Neil Castles' vehicle stopped working on lap 92. Bill Dennis' vehicle had some serious vibration issues on lap 131 while Paul Tyler's engine blew on lap 149. Further engine problems occurred on lap 231 with Buddy Baker, lap 249 with Pete Hamilton, lap 264 with Earl Brooks, lap 302 with Bobby Brack. Friday Hassler gets his third top six finish in a row less than a month after driving the Junior Johnson Chevy to victory at Bristol in relief of Charlie Glotzbach. Richard Petty became a millionaire after this race; this would be the last time a driver won 5 races in a row, in any series, until 2009 when Ron Hornaday won five in a row in the 2009 NASCAR Camping World Truck Series season.

Petty's five consecutive wins during the 1971 NASCAR Winston Cup Series season is considered to be the equivalent of Sebastian Vettel winning nine races in a row at the end of the 2013 Formula One World Championship. Dick Poling would retire from the NASCAR Cup Series after finishing in 26th place during this race. Notable crew chiefs who participated in the race were Junie Donlavey, Harry Hyde, Dale Inman, Vic Ballard, Lee Gordon, John Green; the race car drivers still had to commute to the races using the same stock cars that competed in a typical weekend's race through a policy of homologation. This policy was in effect until 1975. By 1980, NASCAR had stopped tracking the year model of all the vehicles and most teams did not take stock cars to the track under their own power anymore. Section reference: * Driver failed to finish race