August 28475 – The Roman general Orestes forces western Roman Emperor Julius Nepos to flee his capital city, Ravenna. 489 – Theodoric, king of the Ostrogoths, defeats Odoacer at the Battle of Isonzo, forcing his way into Italy. 632 – Fatimah, daughter of the Islamic prophet Muhammad, dies, with her cause of death being a controversial topic among the Sunni Muslims and Shia Muslims. 663 – Silla–Tang armies crush the Baekje restoration attempt and force Yamato Japan to withdraw from Korea in the Battle of Baekgang.
Agathocles of SyracuseAgathocles (Ἀγαθοκλῆς, Agathoklḗs; 361–289 BC) was a Greek tyrant of Syracuse (317–289 BC) and self-styled king of Sicily (304–289 BC). Agathocles was born at Thermae Himeraeae (modern name Termini Imerese), Magna Graecia, in Sicily. The son of a potter who had moved to Syracuse in about 343 BC, he learned his father's trade, but afterwards entered the army along with his brother Antander. In 333 BC he married the widow of his patron Damas, a distinguished and wealthy citizen.
TrigonometryTrigonometry () is a branch of mathematics concerned with relationships between angles and ratios of lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.
AntigenIn immunology, an antigen (Ag) is a molecule, moiety, foreign particulate matter, or an allergen, such as pollen, that can bind to a specific antibody or T-cell receptor. The presence of antigens in the body may trigger an immune response. Antigens can be proteins, peptides (amino acid chains), polysaccharides (chains of simple sugars), lipids, or nucleic acids. Antigens exist on normal cells, cancer cells, parasites, viruses, fungi, and bacteria. Antigens are recognized by antigen receptors, including antibodies and T-cell receptors.
AortaThe aorta (eɪˈɔrtə ; : aortas or aortae) is the main and largest artery in the human body, originating from the left ventricle of the heart, branching upwards immediately after, and extending down to the abdomen, where it splits at the aortic bifurcation into two smaller arteries (the common iliac arteries). The aorta distributes oxygenated blood to all parts of the body through the systemic circulation. In anatomical sources, the aorta is usually divided into sections.
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Sine and cosineIn mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle , the sine and cosine functions are denoted simply as and .
Graph of a functionIn mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane. In the case of functions of two variables, that is functions whose domain consists of pairs the graph usually refers to the set of ordered triples where instead of the pairs as in the definition above. This set is a subset of three-dimensional space; for a continuous real-valued function of two real variables, it is a surface.
EquationIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
