If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

Simpson's paradox for continuous data: a positive trend appears for two separate groups ( blue and red ), a negative trend ( black, dashed ) appears when the data are combined.

In addition to his Taxi work, DeVito voiced Herb Powell, Homer Simpson's half-brother, on two episodes of The Simpsons.

Another derivation constructs Simpson's rule from two simpler approximations: the midpoint rule

The renovation of Simpson's athletic facilities will continue in the future with a proposed design for a new bi-level weight room in the current pool area and two new classrooms in place of the current weight room.

Mike Simpson's goal is to amend title 28, and create the appointment of additional Federal Circuit Judges, to divide the Ninth Judicial Circuit into two smaller judicial circuits.

Lisa Simpson's teacher, who was wearied by all of the reports by the girls of her class about various princesses, said there had been two reports about Princess Ingrid Alexandra.

Gibbs ' Beauforts sank two ships and one of FOS Simpson's submarines sank a third.

Aside from music and romance, the show also chronicles minor but often humorous tribulations of Simpson's life: for example, in episode two she locks her keys in her car, and in episode three she is revealed to be chronically late and she gets lost despite her car having a navigational system, which seems to be of little help.

When the first Michelin Guide to England was published in 1974, no UK restaurant was judged worthy of the maximum three stars, or even two, but Simpson's was one of nine London restaurants, including Le Gavroche, awarded a star.

P. G. Wodehouse devoted several paragraphs of Something New to the restaurant, and in his novel Psmith in the City, his two heroes dine there: " Psmith waited for Mike while he changed, and carried him off in a cab to Simpson's, a restaurant which, as he justly observed, offered two great advantages, namely, that you need not dress, and, secondly, that you paid your half-crown, and were then at liberty to eat till you were helpless, if you felt so disposed, without extra charge.

Fairview Pointe-Claire is a single level mall ; only anchors Simpson's, Eaton's and Pascal's have two floors.

Dr Simpson and two of his friends, Drs Keith and Duncan used to sit every evening in Dr Simpson's dining room to try new chemicals to see if they had any anaesthetic effect.

At that time it included two major Canadian department stores, Simpson's and Eaton's.

Two years later, in 1969, Hoban married Simpson's widow, with whom he has a daughter Daniella, and two stepdaughters Jane and Joanna.

During Simpson's long administration ( 1820-1860 ) the two worked closely together, one in London business circles and the other in the wilds of Canada.

Simpson's vocals in the song span over two octaves from the low note of F < sub > 3 </ sub > to the high note of E < sub > 5 </ sub >.

It concludes that Riviera is a better role model for physicians, whereas Hibbert is a paternalistic and wasteful physician, unlike Riviera, who strives to cut costs and does his best to avoid the coroner, disproving Marge Simpson's claim that he is not a doctor at all.

He is best known for being the most frequent recipient of Bart Simpson's prank calls.

" Simpson's Athabasca Journal reports that on January 1, 1821, " the Festivities of the New Year commenced at four o ' clock this morning when the people honoured me with a salute of fire arms, and in half an hour afterwards the whole Inmates of our Garrison assembled in the hall dressed out in their best clothes, and were regaled in a suitable manner with a few flaggon's Rum and some Cakes.

Simpson's parents, Joe and Tina, appear frequently on the show.

When Lisa Simpson converted to Buddhism, he referred to her as " Marge Simpson's devil-daughter ".

Following Simpson's divorce hearing on 27 October 1936, her solicitor, John Theodore Goddard, became concerned that there would be a " patriotic " citizen's intervention ( a legal device to block the divorce ), and that such an intervention would be successful.

* Mona Simpson's A Regular Guy ( 1996 ) is a fictionalized version of the life of her biological brother, Apple Computers co-founder Steve Jobs.

However, over the span of the first season, Simpson's popularity began growing, as many of her " dumb blonde " antics gave her much publicity.

Clark was on leave from her job following Simpson's acquittal in 1995, and officially resigned in 1997, before the release of her book.

Jordan Schur, the president of Simpson's record label, Geffen, said that " There's no question that it really helped expose her and her music.

Simpson's song " Autobiography ", the title track from her album, plays during the show's opening, which is composed of clips of Simpson from the show mixed with brightly colored backgrounds and handwritten lyrics, words and scribblings.

In episode five, Simpson's backing band is formed and they begin to rehearse for live performances, but Simpson begins to have problems with her vocal cords ; this makes it difficult for her to sing and causes her a great deal of anxiety.

" Shadow " is introduced at the beginning of episode five, when she talks with John Shanks about the song and then begins to sing it while Shanks plays guitar ; this segues into a series of video clips of Simpson's life from her childhood up to the present day, and while these play, Simpson talks about growing up in Texas and being a dancer.

The second episode of the season started with the SNL incident and Simpson's embarrassment over her failed performance and the criticism that followed.

, it remains Simpson's most successful song, and her only song to reach the top ten on the Billboard Hot 100 and the UK Singles Chart.

A more recent example is in Jessica Simpson's music video for her song “ A Public Affair ”, starring Simpson, Christina Applegate, Eva Longoria, Christina Milian, Andy Dick and Ryan Seacrest, and a skating dance crew named Breaksk8.

In February, the song debuted at number 10 on the Australian singles chart ( where it stayed for four weeks ) and at number 98 on the Billboard Hot 100 in the U. S., where it eventually rose to number 86 ; by comparison, Simpson's first single, " Pieces of Me ", had reached number 5 on the Hot 100 a few months earlier, and her second single, " Shadow ", had reached number 57.

Performances of " La La " featured twice in the first season of The Ashlee Simpson Show, Simpson's reality show, which aired in the U. S. on MTV from mid-June to early August 2004: she performed the song during her first live show in episode six, and again at the end of episode seven.

Kaelin came to notice for his role as a minor witness in the trial of O. J. Simpson for the murders of Simpson's ex-wife Nicole Brown Simpson and her friend Ronald Goldman.

On June 27, 2006 MTV Canada aired Making the Video for the first time ( Ashlee Simpson's " Invisible "), but only showed a short clip of the video.

In an episode of MTV's Making the Video on November 23, which documented the making of Simpson's music video for " La La " ( Autobiography < nowiki >'</ nowiki > s third single ) and then premiered it, Simpson mentioned that cameras were there filming for the second season of The Ashlee Simpson Show.

The plot of the episode is also similar to the 1991 video game spin-off from the television series called Bart Simpson's Escape from Camp Deadly.

He also played Ashlee Simpson's boyfriend in the music video for her 2005 song " Boyfriend ".

The video was also nominated at the 2006 MTV Australia Video Music Awards in the category of Best Pop Video, but lost to Ashlee Simpson's " Boyfriend " ( 2005 ).

People magazine called the video " humptastic ", referring to Simpson's progressive sexual image from her previous videos, while an editor for The Irish Independent wrote that Simpson looked " incredibly sexy " in the video.

Craig Seymour of The Buffalo News criticized Simpson's ungraceful performance on the video, which was echoed by Jon Bream and Chris Riemenschneider of The Star Tribune who felt Simpson was trying too hard to be a sexpot in the video.

As the single was released while Simpson's reality show, Newlyweds, was still on air and at the peak of its popularity, the video of the song was created to parallel the show.