“Geometry”方面的作品

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

Ориентация тройки векторов, определение векторного произведения через длину, перпендикулярность и правую тройку, геометрический смысл (площадь параллелограмма), свойства с доказательствами и полный вывод формулы через определитель.

Линейные пространства над произвольным полем, подпространства, линейная зависимость, базис и размерность, сумма и пересечение подпространств, замена базиса.

Аффинные пространства и подпространства, аффинные системы координат и формулы их замены, прямые и плоскости в аффинных пространствах.

Евклидовы и эрмитовы пространства, скалярное произведение, неравенство Коши–Буняковского и неравенство треугольника, ортогональные системы векторов.