# Intrinsic Metrics on Sierpinski-Like Triangles and Their Geometric Properties

## Abstract

**:**

## 1. Introduction

**Definition**

**1.**

## 2. Preliminaries

## 3. The Intrinsic Metric on the Scalene Sierpinski Gasket

**Theorem**

**1.**

**Proof.**

**Case**

**1.**

**Case**

**2.**

**Remark**

**1.**

**Proposition**

**1.**

**Corollary**

**1.**

**Example**

**1.**

## 4. Some Interesting Properties of the Equilateral, Isosceles and Scalene Sierpinski Gaskets

**Proposition**

**2**

**([12]).**

**Example**

**2.**

**Definition**

**2.**

**Remark**

**2.**

**Proposition**

**3.**

**Proof.**

**Remark**

**3.**

**Example**

**3.**

**Corollary**

**2.**

**Proposition**

**4.**

**Proof.**

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The Sierpinski Gaskets constructed on the equilateral, isosceles and scalene triangles respectively.

**Figure 2.**The equilateral Sierpinski Gasket and the sub-triangle ${S}_{\sigma}$ where $\sigma ={w}_{1}{w}_{2}\dots {w}_{n}$.

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**MDPI and ACS Style**

Saltan, M.
Intrinsic Metrics on Sierpinski-Like Triangles and Their Geometric Properties. *Symmetry* **2018**, *10*, 204.
https://doi.org/10.3390/sym10060204

**AMA Style**

Saltan M.
Intrinsic Metrics on Sierpinski-Like Triangles and Their Geometric Properties. *Symmetry*. 2018; 10(6):204.
https://doi.org/10.3390/sym10060204

**Chicago/Turabian Style**

Saltan, Mustafa.
2018. "Intrinsic Metrics on Sierpinski-Like Triangles and Their Geometric Properties" *Symmetry* 10, no. 6: 204.
https://doi.org/10.3390/sym10060204