# Constructions of Helicoidal Surfaces in Euclidean Space with Density

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

## 3. Main Theorems and Examples

#### 3.1. The Solution of Equation (5)

**Theorem**

**1.**

**Corollary**

**1.**

**Proof.**

**Example**

**1.**

**Example**

**2.**

#### 3.2. The Solution of Equation (6)

**Theorem**

**2.**

**Example**

**3.**

**Example**

**4.**

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**A helicoidal surface with ${G}_{\varphi}(u)=\frac{2{u}^{2}-1}{{({u}^{4}-{u}^{2}-1)}^{2}}-4.$

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**MDPI and ACS Style**

Yoon, D.W.; Kim, D.-S.; Kim, Y.H.; Lee, J.W.
Constructions of Helicoidal Surfaces in Euclidean Space with Density. *Symmetry* **2017**, *9*, 173.
https://doi.org/10.3390/sym9090173

**AMA Style**

Yoon DW, Kim D-S, Kim YH, Lee JW.
Constructions of Helicoidal Surfaces in Euclidean Space with Density. *Symmetry*. 2017; 9(9):173.
https://doi.org/10.3390/sym9090173

**Chicago/Turabian Style**

Yoon, Dae Won, Dong-Soo Kim, Young Ho Kim, and Jae Won Lee.
2017. "Constructions of Helicoidal Surfaces in Euclidean Space with Density" *Symmetry* 9, no. 9: 173.
https://doi.org/10.3390/sym9090173