# Do You Really Know Convex Geometry?

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In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory, etc.

• 1.

### Convex geometry is a course under .......?

• A.

Mathematics

• B.

Music

• C.

Language

• D.

History

A. Mathematics
Explanation
Convex geometry is a branch of mathematics that focuses on the study of convex sets, which are sets that contain all the line segments connecting any two points within the set. It involves the study of various properties and characteristics of convex sets, such as convex hulls, convex functions, and convex optimization. Therefore, the correct answer is Mathematics.

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• 2.

### Convex Geometry is a branch of ....?

• A.

Algebra

• B.

Number theory

• C.

Geometry

• D.

Space

C. Geometry
Explanation
Convex Geometry is a branch of Geometry. It specifically deals with the study of convex sets, which are sets that contain all the line segments connecting any two points within the set. This branch of geometry focuses on properties and characteristics of convex shapes, such as convex polygons and convex polyhedra. It explores concepts like convex hulls, convex functions, and convex optimization. Convex Geometry plays a crucial role in various fields, including computer science, optimization theory, and operations research.

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• 3.

### Convex Geometry is the branch of geometry studying .....?

• A.

Convex sets

• B.

Linear algebra

• C.

Vector spaces

• D.

Lattices

A. Convex sets
Explanation
Convex Geometry is the branch of geometry that focuses on studying convex sets. Convex sets are defined as sets where, for any two points within the set, the line segment connecting them is also completely contained within the set. This branch of geometry analyzes the properties and characteristics of convex sets, including their boundaries, intersections, and transformations. It is a fundamental concept in mathematics and has applications in various fields such as optimization, computer graphics, and operations research.

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• 4.

### Convex Geometry is the branch of geometry studying convex sets, mainly in .....?

• A.

Linear algebra

• B.

Lattices

• C.

Vector space

• D.

Euclidean space

D. Euclidean space
Explanation
Convex Geometry is the branch of geometry that studies convex sets, which are sets that contain all the line segments connecting any two points within the set. Euclidean space refers to the standard three-dimensional space that we are familiar with, where points are represented by coordinates and distances are measured using the Euclidean metric. Therefore, Euclidean space is the most appropriate setting for studying convex sets and their properties.

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• 5.

### Convex sets occur naturally in all areas in the options except .......

• A.

Linear programmimg

• B.

Discrete geometry

• C.

Convex analysis

• D.

Linear algebra

D. Linear algebra
Explanation
Convex sets occur naturally in all areas mentioned except for linear algebra. While linear algebra deals with vector spaces, matrices, and linear transformations, it does not specifically focus on the study of convex sets. On the other hand, convex sets are fundamental in linear programming, discrete geometry, and convex analysis, as they play a crucial role in optimization, geometric structures, and the study of convex functions, respectively. Therefore, linear algebra is the only option that does not naturally involve the study of convex sets.

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• 6.

### The mathematical discipline Convex and Discrete Geometry includes how many major branches?

• A.

3

• B.

4

• C.

5

• D.

1

A. 3
Explanation
Convex and Discrete Geometry includes three major branches. This implies that the discipline focuses on three distinct areas of study within mathematics.

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• 7.

### General convexity is subdivided in how many parts?

• A.

18

• B.

20

• C.

19

• D.

15

A. 18
Explanation
General convexity is subdivided into 18 parts.

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• 8.

### Convex geometry became an independent branch of mathematics at the turn of the .....?

• A.

20th Century

• B.

18th Century

• C.

12th Century

• D.

19th Century

A. 20th Century
Explanation
Convex geometry became an independent branch of mathematics at the turn of the 20th Century. This means that it gained recognition and significance as a separate field of study during this time period. Prior to the 20th Century, convex geometry may have been studied within the broader context of geometry, but it was not considered a distinct area of focus.

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• 9.

### In what year did a give a comprehensive survey of convex geometry in Euclidean space?

• A.

1918

• B.

1970

• C.

1934

• D.

1960

C. 1934
Explanation
In 1934, a comprehensive survey of convex geometry in Euclidean space was given.

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• 10.

### In 1934 who gave a comprehensive survey of convex geometry in Euclidean space?

• A.

T. Bonnesen and W. Fenchel

• B.

Isaac Newton

• C.

Albert Einstein

• D.

James McCaffrey