Highland Park is a suburban city in Lake County, United States, about 25 miles north of downtown Chicago. As of the 2018 population estimate, the population was 29,622. Highland Park is one of several municipalities located on the North Shore of the Chicago metropolitan area. In 1867, ten men purchased Highland Park for $39,198.70. They were the original stockholders of the Highland Park Building Company. Following construction of the Chicago and Milwaukee Railroad, a depot was established at Highland Park and a plat, extending south to Central Avenue, was laid out in 1856. Highland Park was established as a city on March 11, 1869, with a population of 500, evolved from two settlements—St. John and Port Clinton. Highland Park was named from its parklike setting at a lofty elevation relative to the lake, was given its name from Walter S. Gurnee; the town annexed the village of Ravinia in 1899. Highland Park has several attractions including a vibrant downtown shopping district and the Ravinia Festival.

Ravinia Festival is an open-air pavilion seating 3,200, which hosts classical and jazz concerts in the summers. It has been the summer home of the Chicago Symphony Orchestra since 1936. Concert-goers can purchase seats in tickets to sit on the lawn. Many visitors arrive picnic on the lawn before and during concerts; the festival is located in Ravinia District an artists' colony, which still retains much of its early character and architecture. Highland Park has several landmark structures listed in the National Register of Historic Places, notably the Willits House by Frank Lloyd Wright. In addition to several houses designed by Wright, the National Register lists homes designed by prominent architects including John S. Van Bergen, Howard Van Doren Shaw, Robert E. Seyfarth, David Adler. Landscape architect Jens Jensen lived in Highland Park and designed a number of projects in the community that are listed on the register. There are three public beaches in Highland Park: Rosewood Beach, Moraine Beach and Park Avenue Beach.

Highland Park is home to the North Shore Yacht Club. According to the U. S. Census Bureau, the city has a total area of 12.2 square miles, of which 12.2 square miles is land and 0.039 square miles, or 0.27%, is water. Its geographic features include a 100-foot-high bluff running along 6 miles of Lake Michigan shoreline and deep, wooded ravines extending up to 1 mile inland. Elevations range from 580 to 725 feet above sea level; as of the 2010 United States Census, there were 29,763 people living in the city. The racial makeup of the city was 91.05% White, 1.84% Black or African American, 2.9% Asian, 0.18% Native American, 0.03% Pacific Islander, 2.51% of some other race and 1.48% of two or more races. 7.28 % were Latino. As of the census of 2000, there were 31,365 people, 11,521 households, 8,917 families living in the city; the population density was 2,537.5 people per square mile. There were 11,934 housing units at an average density of 965.5/sq mi. The racial makeup of the city was 91.20% White, 1.78% African American, 0.08% Native American, 2.28% Asian, 0.01% Pacific Islander, 3.46% from other races, 1.18% from two or more races.

Hispanic or Latino of any race were 8.90% of the population. There were 11,521 households out of which 36.9% had children under the age of 18 living with them, 69.9% were married couples living together, 5.8% had a female householder with no husband present, 22.6% were non-families. 19.5% of all households were made up of individuals and 9.3% had someone living alone, 65 years of age or older. The average household size was 2.71 and the average family size was 3.09. In the city the population was spread out with 27.0% under the age of 18, 4.6% from 18 to 24, 25.5% from 25 to 44, 27.8% from 45 to 64, 15.1% who were 65 years of age or older. The median age was 41 years. For every 100 females, there were 95.9 males. For every 100 females age 18 and over, there were 92.5 males. The median income for a household in the city was $100,967, the median income for a family was $317,235. Males had a median income of $83,121 versus $41,175 for females; the per capita income for the city was $55,331. About 2.3% of families and 3.8% of the population were below the poverty line, including 3.9% of those under age 18 and 3.1% of those age 65 or over.

Highland Park is governed by the council-manager form of government. The non-partisan City Council consists of seven members, including an elected mayor and six councilmembers, all elected at-large and serving staggered four-year terms; the current city council consists of: Highland Park is considered a Democratic stronghold. Highland Park voters overwhelmingly voted for Illinois Senator Barack Obama in the 2008 presidential election, choosing him over Arizona Senator John McCain, 76.3%–23.1%. Highland Park voters tend to prefer Democrats in local races. At the state level, Highland Park is a part of the 58th House District, represented by Bob Morgan, the 29th Senate District, represented by Julie Morrison. At the county level, the city is split between Districts 11 and 12, represented by former Highland Park City Councilman Paul Frank and former Lake Forest Mayor Mike Rummel, respectively; the international headquarters of Solo Cup Company used to be located in Highland Park, before relocating to neighboring Lake Forest in 2009.

The main highway in Highland Park is US-41. Commuter rail is available at four Metra stations within city borders, as

Svatopluk Habanec is a Czech former football player and manager of Třinec. His playing position was defender. Habanec scored 11 goals in 28 games in the 2000–01 Czech 2. Liga, finishing among the leading scorers of the league, he was announced as the new manager of Ústí nad Labem on 19 September 2007. He guided Ústí to the Czech First League after masterminding a second-place finish for the club in the 2009–10 Czech 2. Liga. Despite their relegation from the Czech First League in 2010/11, Habanec won the Czech 2. Liga with Ústí the following season. In August 2012, Habanec was appointed as the successor to Miroslav Soukup at Czech First League side 1. FC Slovácko. Ústí nad LabemCzech 2. Liga Winners: 2011–12 Czech 2. Liga Runners-Up: 2009–10 Manager Profile at idnes.cz Player Profile at idnes.cz Profile at fkusti.cz

In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point. The concept was first studied by William Kingdon Clifford in elliptic space and appears only in spaces of at least three dimensions. Since parallel lines have the property of equidistance, the term "parallel" was appropriated from Euclidean geometry, although the "lines" of elliptic geometry are geodesic curves and, unlike the lines of Euclidean geometry, are of finite length; the algebra of quaternions provides a descriptive geometry of elliptic space in which Clifford parallelism is made explicit. The lines on 1 in elliptic space are described by versors with a fixed axis r: For an arbitrary point u in elliptic space, two Clifford parallels to this line pass through u; the right Clifford parallel is, the left Clifford parallel is. Rotating a line about another, to which it is Clifford parallel, creates a Clifford surface; the Clifford parallels through points on the surface.

A Clifford surface is thus a ruled surface since every point is on two lines, each contained in the surface. Given two square roots of minus one in the quaternions, written r and s, the Clifford surface through them is given by. Clifford parallels were first described in 1873 by the English mathematician William Kingdon Clifford. In 1900 Guido Fubini wrote his doctoral thesis on Clifford's parallelism in elliptic spaces. In 1931 Heinz Hopf used. In 2016 Hans Havlicek showed that there is a one-to-one correspondence between Clifford parallelisms and planes external to the Klein quadric. Clifford torus Laptev, B. L. & B. A. Rozenfel'd Mathematics of the 19th Century: Geometry, page 74, Birkhäuser Verlag ISBN 3-7643-5048-2. J. A. Tyrrell & J. G. Semple Generalized Clifford Parallelism, Cambridge University Press ISBN 0-521-08042-8. Duncan Sommerville The Elements of Non-Euclidean Geometry, page 108 Paratactic lines, George Bell & Sons