What Do You Know About Conic Sections?

Explanation
The correct answer is three because there are three types of conic sections: the ellipse, the parabola, and the hyperbola. These are geometric curves that can be formed by intersecting a cone with a plane at different angles and positions. Each type of conic section has its own unique characteristics and equations that describe its shape. Therefore, there are three distinct types of conic sections.

Explanation
The conic sections, which include the circle, ellipse, parabola, and hyperbola, were extensively studied by ancient Greek mathematicians. They made significant contributions to the understanding and properties of these curves, with prominent mathematicians such as Euclid, Apollonius of Perga, and Archimedes delving into the subject. Their work laid the foundation for the development of conic section theory and its applications in various fields of mathematics and science.

Explanation
The conic sections were extensively studied by ancient Greek mathematicians, and their work on this subject reached its peak around 200 B.C. During this time, mathematicians such as Euclid and Apollonius made significant contributions to the understanding and classification of conic sections, including the properties of ellipses, parabolas, and hyperbolas. Their work laid the foundation for further advancements in geometry and calculus.

Explanation
Apollonius of Perga is credited with making the greatest progress in the study of conics by the ancient Greeks. He is known for his work "Conics," in which he extensively studied and classified different types of conic sections, including the ellipse, parabola, and hyperbola. Apollonius' work laid the foundation for the modern understanding of conic sections and their properties. His contributions greatly advanced the field of mathematics and had a lasting impact on the study of conics.

Explanation
Pappus of Alexandr is credited with expounding on the importance of the concept of a conic's focus and detailing the related concept of a directrix, including the case of the parabola. This means that Pappus of Alexandr contributed to the understanding of the geometric properties of conic sections, specifically focusing on the focus and directrix of these curves. This knowledge was lacking in the known works of Apollonius, another important mathematician of the time. Therefore, Pappus of Alexandr is the correct answer as he made significant contributions to the study of conic sections.

Explanation
The correct answer is 1000 CE. This means that an instrument for drawing conic sections was first described in the year 1000 CE.

Explanation
Al-Kuhi, an Islamic mathematician, is credited with describing the instrument for drawing conic sections in 1000 CE. This instrument was a significant development in mathematics and allowed for the accurate construction of conic sections, which are important curves in geometry. Al-Kuhi's contribution in describing this instrument showcases the advancements made by Islamic mathematicians during the medieval period.

Explanation
Johannes Kepler extended the theory of conics through the "principle of continuity", which is a precursor to the concept of limits. This means that Kepler built upon the existing understanding of conics and developed the idea of continuity, which eventually led to the concept of limits. Although Albert Einstein, Isaac Newton, and Bill Nye are all notable figures in their respective fields, they did not specifically contribute to the extension of the theory of conics through the principle of continuity.

Explanation
Mathematics is usually studied in school because it is a fundamental subject taught in educational institutions. Schools provide a structured environment with qualified teachers who can teach and guide students in understanding mathematical concepts and solving problems. Additionally, schools have resources such as textbooks, classrooms, and interactive tools that facilitate the learning and practice of mathematics. Therefore, it is the most appropriate and common place for students to study mathematics.