Parliament House, Melbourne

Parliament House is the meeting place of the Parliament of Victoria, one of the parliaments of the Australian states and territories. Located on Spring Street on the edge of the Hoddle Grid, the grand colonnaded front dominates the vista up Bourke Street. Construction began in 1855, the first stage was opened the following year, with various sections completed over the following decades. Between 1901 and 1927, it served as the meeting place of the Parliament of Australia, during the period when Melbourne was the temporary national capital; the building is listed on the Victorian Heritage Register. The Victorian gold rush and population boom led calls for greater democracy and a home for political debate in Victoria. Prior to the Colony of Victoria acquiring self-government in 1851, Governor Charles La Trobe instructed Surveyor General Robert Hoddle to select a site for the colony's new parliament to meet. Hoddle selected a site on the eastern hill at the top of Bourke Street, which commanded a view over the entire city.

It was not until April 1854 that Eastern Hill, the current Spring Street site, was formally agreed to due to ongoing disagreements over the best location. The exact sequence of events is unclear, with a number of architects and designs chosen and rejected in succession, with the final result based on earlier work; the first design appeared as early as 1851 by Colonial Architect Henry Ginn. A design by Smith & Pritchard won first prize; the Colony's newly arrived Chief Engineer Captain Pasley was asked to prepare a design by April 1854 for a unicameral building, which may have been soon reworked into one for a bi-cameral Parliament, which had just been decided upon. A design was published in c1854 showing a restrained Palladian building much like the recently started State Library of Victoria. John Knight and Peter Kerr had just formed a partnership, Knight may still have been an architect within the Public Works Department at this time, while practicing privately; this design was apparently deemed unsuitable, Knight & Kerr were employed separately to create a much grander design by 1855, mainly a reworking of the 1854 design.

This design is extraordinarily impressive and elaborate for a fledgling colony, albeit one flush with the results of the recent gold rush. It featured a columned screen on at least three sides, with end and central bays set forward, statuary atop the cornice, grand stairs, a tall multi-stage columned and domed tower. Images of this design were published, photographs exist of a model of the scheme. Knight & Kerr are credited with the design of the first stages of Parliament House when construction commenced in 1855, it was decided to construct the building in stages, owing to its vast size and cost, so construction began in December 1855 on only the two chambers, one for the Victorian Legislative Assembly and a smaller more ornate chamber for the Victorian Legislative Council. Construction progressed and on 25 November 1856, the first session of the Victorian Government in the new chambers was opened, to great acclaim. Construction of the Library and eastern wing began in 1858 and was completed in 1860.

There was much debate about an appropriate stone for the exterior, with a desire to use stone from Victoria, though none could be found that were known to be suitable. Bluestone was rejected as too dark and sombre, local granite as too expensive Carrara marble was considered, but freestone from Bacchus Marsh was chosen; this proved to decay and large parts had to be replaced with stone from Tasmania within a few years. With the library complete, the two legislative chambers were joined at the rear, resulting in a `U-shaped' building; the classical architectural detail of the east facade were noted as the first expression of Peter Kerr's vision for the building. No further construction took place for 18 years. In 1876 a Royal Commission was formed to recommend the next steps, it tabled several changes, including the addition of a large dome, the appointment of Peter Kerr as leading architect, a resumption of construction. Kerr produced new plans for the completion of the building in 1877, replacing the tower with a dome, replacing the complex external architecture with a simpler design dominated by a long colonnade.

This is the design, known and referred to as the'original' design. The Great Hall and vestibule were completed in 1879, with the Commission continuing to produce reports on the progress, their report of 1878 noted the progress on the construction of the Queens Hall and Vestibule, that there was still no agreement on a suitable stone for the exterior. Queen's Hall was used for formal receptions and banquets, while the Vestibule offered a formal entry to Parliament House, though the grand front steps were not to be completed for another decade. Planning for the construction of the grand classical colonnaded front of the building facing Bourke Street as envisaged in the 1877 plan was to follow on after the completion of the previous section, but construction was delayed by the ongoing desire to find a suitable Victorian stone for the exterior. Work in interiors progressed, with the imported Minton tiled flo

Dongjiao 82-class dispatch boat

Dongjiao 82 class dispatch boat is a class of naval auxiliary ship in service with the People's Liberation Army Navy. The name of this class is after the first unit commissioned, with the exact type still remains unknown, only a single unit of this class have been confirmed in active service as of mid-2010s. Dongjiao 82 class series ships in PLAN service are designated by a combination of two Chinese characters followed by three-digit number; the second Chinese character is Jiao, short for Jiao-Tong-Ting, meaning dispatch boat in Chinese, because these ships are classified as dispatch boats. The first Chinese character denotes which fleet the ship is service with, with East for East Sea Fleet, North for North Sea Fleet, South for South Sea Fleet. However, the pennant numbers may have changed due to the change of Chinese naval ships naming convention

Carnot's theorem (inradius, circumradius)

In Euclidean geometry, Carnot's theorem states that the sum of the signed distances from the circumcenter D to the sides of an arbitrary triangle ABC is D F + D G + D H = R + r, where r is the inradius and R is the circumradius of the triangle. Here the sign of the distances is taken to be negative if and only if the open line segment DX lies outside the triangle. In the diagram, DF is negative and both DG and DH are positive; the theorem is named after Lazare Carnot. It is used in a proof of the Japanese theorem for concyclic polygons. Claudi Alsina, Roger B. Nelsen: When Less is More: Visualizing Basic Inequalities. MAA, 2009, ISBN 978-0-88385-342-9, p.99 Frédéric Perrier: Carnot's Theorem in Trigonometric Disguise. The Mathematical Gazette, Volume 91, No. 520, pp. 115–117 David Richeson: The Japanese Theorem for Nonconvex Polygons – Carnot's Theorem. Convergence, December 2013 Weisstein, Eric W. "Carnot's theorem". MathWorld. Carnot's Theorem at cut-the-knot Carnot's Theorem by Chris Boucher; the Wolfram Demonstrations Project