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Just like the name indicates, almost integers are numbers that are not integer but very close to one. It is used in several branches of mathematics and you've probably used them or heard of them before. Try our quiz to verify if you have enough knowledge about these numbers.

• 1.

### What's a modular form?

• A.

It is a function on the upper half plane satisfying a certain kind of functional equation

• B.

It is an analytic function on the upper half plane satisfying a certain kind of functional equation

• C.

It is a function on the lower half plane satisfying a certain kind of functional equation

• D.

It is a function on the upper plane satisfying all kinds of functional equation

B. It is an analytic function on the upper half plane satisfying a certain kind of functional equation
Explanation
A modular form is defined as an analytic function on the upper half plane that satisfies a specific type of functional equation. This means that the function must meet certain conditions and properties in order to be classified as a modular form. The answer choice "It is an analytic function on the upper half plane satisfying a certain kind of functional equation" accurately describes the definition of a modular form.

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• 2.

### In which branch of mathematics can they be found?

• A.

Algebra

• B.

Geometry

• C.

Probabilities

• D.

Recreational mathematics

D. Recreational mathematics
Explanation
Recreational mathematics is a branch of mathematics that focuses on puzzles, games, and mathematical recreations that are not directly related to practical applications. It includes activities like solving puzzles, playing games, and exploring mathematical patterns for the sake of enjoyment and intellectual curiosity. While algebra, geometry, and probabilities are more formal branches of mathematics with practical applications, recreational mathematics is more about exploring the fun and playful side of math.

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• 3.

### What is an integer?

• A.

It is numbers ranked between 10 and 9

• B.

It is numbers ranked between 1 and 9

• C.

It is a number that can be written without a fractional component

• D.

It is a number inferior to 100

C. It is a number that can be written without a fractional component
Explanation
An integer is a whole number that can be written without any decimal or fractional component. It includes both positive and negative numbers, as well as zero. Integers are not limited to a specific range, such as being ranked between 10 and 9 or being inferior to 100. Therefore, the correct answer is that an integer is a number that can be written without a fractional component.

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• 4.

### What are the well-known examples of almost integers?

• A.

Logarithms

• B.

High powers of golden ratio.

• C.

Fractions

• D.

Cardinals

B. High powers of golden ratio.
Explanation
High powers of the golden ratio are well-known examples of almost integers because as the power of the golden ratio increases, the resulting number gets closer and closer to an integer. The golden ratio, denoted by the symbol Ï† (phi), is approximately equal to 1.618. When this value is raised to a high power, the decimal part becomes very small, making it almost an integer. This property of the golden ratio is often seen in various mathematical and natural phenomena, such as in the spirals of certain plants and the proportions of ancient Greek architecture.

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• 5.

### What's the particularity of a golden ratio?

• A.

It is that it is multiple of 5

• B.

It is that it is lower than 100

• C.

It's that it is a Piso-Vijayaraghavan number

• D.

It is that it is higher than 100

C. It's that it is a Piso-Vijayaraghavan number
• 6.

### What is a Pisot-Vijayaraghavan number?

• A.

It is a real algebraic number greater than 10

• B.

It is a real algebraic number greater than 5

• C.

It is a real algebraic number greater than 1

• D.

It is a real algebraic number greater than 2

C. It is a real algebraic number greater than 1
Explanation
A Pisot-Vijayaraghavan number is a real algebraic number greater than 1.

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• 7.

### What ratios are known to make almost integers?

• A.

The ratios of Fibonacci

• B.

The ratios of Mancini

• C.

The ratios of Newton

• D.

The ratios of Einstein

A. The ratios of Fibonacci
Explanation
The Fibonacci sequence is a mathematical sequence where each number is the sum of the two preceding ones. The ratios between consecutive Fibonacci numbers tend to approach the golden ratio, which is approximately 1.618. This ratio is known to create aesthetically pleasing and harmonious proportions, often found in art, architecture, and nature. Due to the close approximation to whole numbers, the ratios of Fibonacci numbers are considered to make almost integers.

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• 8.

### From where did the ratios of Fibonacci originated from?

• A.

Italy

• B.

Indian mathematics

• C.

Chinese Algebra

• D.

Germany

B. Indian mathematics
Explanation
The ratios of Fibonacci originated from Indian mathematics. Fibonacci, an Italian mathematician, was introduced to the Fibonacci sequence and its ratios while studying mathematical concepts in India during the 13th century. He then brought this knowledge back to Europe and popularized it through his book "Liber Abaci". The Fibonacci sequence and its ratios have since become well-known and widely studied in mathematics.

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• 9.

### What's an Eisenstein series?

• A.

They are numerical forms with infinite series

• B.

They are modular forms with infinite series

• C.

They are particular modular forms with infinite series

• D.

They are particular modular forms with limited series

C. They are particular modular forms with infinite series
Explanation
Eisenstein series are a type of modular forms with infinite series. Unlike other modular forms, which have certain restrictions or conditions, Eisenstein series are specific modular forms that have an infinite series representation. These series play an important role in various areas of mathematics, including number theory and complex analysis.

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• 10.

### What's a modular form?

• A.

It is a function on the upper half plane satisfying a certain kind of functional equation

• B.

It is an analytic function on the upper half plane satisfying a certain kind of functional equation

• C.

It is a function on the lower half plane satisfying a certain kind of functional equation

• D.

It is a function on the upper plane satisfying all kinds of functional equation

B. It is an analytic function on the upper half plane satisfying a certain kind of functional equation
Explanation
A modular form is defined as an analytic function on the upper half plane that satisfies a certain kind of functional equation. This means that the function must have certain properties and relationships with other functions in order to be considered a modular form. The answer choice "It is an analytic function on the upper half plane satisfying a certain kind of functional equation" accurately describes the definition of a modular form.

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• 11.

### What is a mathematical coincidence?

• A.

It is one that occurs when 6 expressions show a near-equation which has no theoretical explanation

• B.

It is one that occurs when 3 expressions show an equation which has no theoretical explanation

• C.

It is one that occurs when 2 expressions show a near-equation which has no theoretical explanation

• D.

It is one that occurs when 4 expressions show a near-equation which has no theoretical explanation

C. It is one that occurs when 2 expressions show a near-equation which has no theoretical explanation
Explanation
A mathematical coincidence refers to a situation where two expressions exhibit a near-equation without any underlying theoretical explanation. In other words, it is a coincidence that these two expressions appear to be almost equal without any logical reason or mathematical relationship between them.

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• Current Version
• Mar 19, 2023
Quiz Edited by
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• May 15, 2018
Quiz Created by
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