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HSC - Mathematics. Masudur Rahman Mathematics Academy
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49CONIC SECTIONS:A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a pl...
19/07/2025

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CONIC SECTIONS:
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.

History:
Conic Sections ( Circle, Ellipse, Parabola and Hyperbolas) were first studied by ancient Greek mathematicians, with Menaechmus credited as the earliest discoverer around 350 BCE while working on the problem of doubling the cube. These curves were further investigated by Euclid, Archimedes, and later by Apollonius of Perga, who is known for his comprehensive work on conics in his eight-book series. Later, mathematicians like Pappus, Omar Khayyam, and even Descartes contributed to the understanding and application of conic sections.

Basic Definition:
CONIC SECTIONS
•A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane; the three types are parabolas, ellipses, and hyperbolas. A conic section can be graphed on a coordinate plane. Every conic section has certain features, including at least one focus and directrix. Parabolas have one focus and directrix, while ellipses and hyperbolas have two of each.

- Circle
•A circle is the set of all points in a plane that are equidistant from a fixed point called the center.

- Parabola
•A parabola is the set of all points in a plane that are equidistant from a fixed point (focus) and a fixed line (directrix).

- Ellipse
•An ellipse is the set of all points in a plane where the sum of the distances from two fixed points (foci) is constant.

- Hyperbola
•A hyperbola is the set of all points in a plane where the absolute difference of the distances from two fixed points (foci) is constant.

Properties and formula:
📐 C

48Four types of Calculus notations:1. Leibniz notation2. Lagrange notation3. Euler notation and4. Newton notation
11/07/2025

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Four types of Calculus notations:
1. Leibniz notation
2. Lagrange notation
3. Euler notation and
4. Newton notation

12/06/2025

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02/06/2025

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45আমাদের ক্লাসগুলো এমনভাবে সাজানো যে, ম্যাথগুলোর মধ্যে যত বৈচিত্র্য সম্ভব সবটাই কাভার করা, যাতে শিক্ষার্থীদের বেসিক ক্লি...
21/05/2025

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আমাদের ক্লাসগুলো এমনভাবে সাজানো যে, ম্যাথগুলোর মধ্যে যত বৈচিত্র্য সম্ভব সবটাই কাভার করা, যাতে শিক্ষার্থীদের বেসিক ক্লিয়ার হয় এবং যা তাদের এডমিশনেও এগিয়ে রাখে। টপিক শেষে রয়েছে অফলাইন এক্সাম।
🛑 শুধু এ+ নয় টার্গেট এখন ১০০!

15/05/2025

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416 Father of Branch of Mathematics WHO changed the world.1. Archemedes: Father of Mathematics, Archimedes was the great...
02/05/2025

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6 Father of Branch of Mathematics WHO changed the world.
1. Archemedes: Father of Mathematics, Archimedes was the greatest mathematician of his age. His contributions in geometry revolutionised the subject and his methods anticipated the integral calculus. He was a practical man who invented a wide variety of machines including pulleys and the Archimidean screw pumping device.

2. Euclid: Father of Geometry, Euclid was a Greek mathematician best known for his treatise on geometry: The Elements. This influenced the development of Western mathematics for more than 2000 years.

3.Al'Khwarizmi: Father of Algebra, Al'Khwarizmi was an Islamic mathematician who wrote on Hindu-Arabic numerals. The word algorithm derives from his name. His algebra treatise Hisab al-jabr w'al-muqabala gives us the word algebra and can be considered as the first book to be written on algebra.

4. Issac Newton: Father of Calculus, Isaac Newton was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.

5. Carl Friedrich Gauss: Prince of Mathematics, Carl Friedrich Gauss worked in a wide variety of fields in both mathematics and physics incuding number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. His work has had an immense influence in many areas.

6. Leonhard Euler: King of Mathematics, Leonhard Euler was a Swiss mathematician who made enormous contributions to a wide range of mathematics and physics including analytic geometry, trigonometry, geometry, calculus and number theory.

Source: Mac Tutor

19/04/2025

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Review of Geometry π is equal to 180°

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