Hawaiʻiloa is the settler of the island of Hawai'i based on an ancient Hawaiian legend. According to the legend, Hawaiʻiloa was navigator. While out with a crew of men, they accidentally stumbled upon the island of Hawaiʻi, named in Hawaiʻiloa's honor. Hawaiʻiloa returned to his homeland of Ka ʻāina kai melemele a Kane, "the land of the yellow sea of Kane" in order to bring his family back with him to Hawai'i, he organized a colonizing expedition with his family and eight other skilled navigators. They settled on; the legend contains reference to his children: Maui, Kauaʻi, Oʻahu who settled on the islands that bear their names. The story of Hawaiʻiloa has received a great deal of attention from modern Hawaiians, as a realistic depiction of the settling of the islands, consistent with current anthropological and historical beliefs. Many people believe. However, the story of Hawaiʻiloa is attested only by late sources, such as the antiquarians Abraham Fornander and Thomas George Thrum; as they did not give their original Hawaiian sources, but only digests and compilations, we cannot be sure that the tale has not been slanted towards proof of Fornander's now discredited migration theories, or that it has not been elaborated by 19th century Hawaiians eager to stress the validity of their own beliefs.

Hawaiʻiloa is not mentioned in early Hawaiian historian sources like Samuel Kamakau. Malo says there are many stories about the origin of the Hawaiians and cites some migration tales and some legends of indigenous origin, he does not mention Hawaiʻiloa. Kamakau says that the first man and woman were Hulihonua and Keakahuilani, that they were created on Oʻahu. Hawaiʻiloa is the name of a voyaging canoe. Thought to be named after the legendary navigator, the canoe was built and sailed for international navigation; the canoe Hawaiʻiloa is now docked at Honolulu Harbor. It is sailed on long voyages throughout the Pacific Ocean in hopes of studying voyaging techniques used in Ancient Hawaii. Hawaiki Hawaiian religion Hōkūleʻa Polynesian navigation Polynesian Voyaging Society

Barrow's inequality

In geometry, Barrow's inequality is an inequality relating the distances between an arbitrary point within a triangle, the vertices of the triangle, certain points on the sides of the triangle. It is named after David Francis Barrow. Let P be an arbitrary point inside the triangle ABC. From P and ABC, define U, V, W as the points where the angle bisectors of BPC, CPA, APB intersect the sides BC, CA, AB, respectively. Barrow's inequality states that P A + P B + P C ≥ 2, with equality holding only in the case of an equilateral triangle. Barrow's inequality can be extended to convex polygons. For a convex polygon with vertices A 1, A 2, …, A n let P be an inner point and Q 1, Q 2, …, Q n the intersections of the angle bisectors of ∠ A 1 P A 2, …, ∠ A n − 1 P A n, ∠ A n P A 1 with the associated polygon sides A 1 A 2, …, A n − 1 A n, A n A 1 the following inequality holds: ∑ k = 1 n | P A k | ≥ sec ⁡ ∑ k = 1 n | P Q k | Here sec ⁡ denotes the secant function. For the triangle case n = 3 the inequality becomes Barrow's inewuality due to sec ⁡ = 2.

Barrow's inequality strengthens the Erdős–Mordell inequality, which has identical form except with PU, PV, PW replaced by the three distances of P from the triangle's sides. It is named after David Francis Barrow. Barrow's proof of this inequality was published in 1937, as his solution to a problem posed in the American Mathematical Monthly of proving the Erdős–Mordell inequality; this result was named "Barrow's inequality" as early as 1961. A simpler proof was given by Louis J. Mordell. Euler's theorem in geometry List of triangle inequalities Hojoo Lee: Topics in Inequalities - Theorems and Techniques

Joe Brown (footballer, born 1988)

Joseph William Brown is an English footballer, who plays for Bradford Park Avenue. Brown signed for Bradford City as an apprentice in 2004, he made his debut for the Bantams in a Football League Trophy first-round game at Morecambe on 22 November 2005 when he came on as an 82nd-minute substitute. He scored a last-minute winner. In the second round he was again a scoring substitute but Bradford lost 2–1, his league debut came in December in a goalless draw at Scunthorpe United. He scored his one and only league goal for Bradford – again in the 90th minute – after coming on as substitute against Blackpool in March; the following season, he again scored a Football League Trophy goal. Brown was given a three-match suspension after losing his appeal against a red-card in Bradford's 4–1 loss against Blackpool and was released by City at the end of the 2006–07 season after making just seven appearances, he went on trial with York City at the end of the 2006–07 season but was deemed "no better than what we have got" by manager Billy McEwan.

He had a trial with Halifax Town and trained with several league clubs, but joined Bradford Park Avenue in August 2007. Joe Brown at Soccerbase