 1628881800

# JavaScript Algorithms and Data Structures: Math - Liu Hui π Algorithm

Liu Hui remarked in his commentary to The Nine Chapters on the Mathematical Art, that the ratio of the circumference of an inscribed hexagon to the diameter of the circle was three, hence π must be greater than three. He went on to provide a detailed step-by-step description of an iterative algorithm to calculate π to any required accuracy based on bisecting polygons; he calculated π to between 3.141024 and 3.142708 with a 96-gon; he suggested that 3.14 was a good enough approximation, and expressed π as 157/50; he admitted that this number was a bit small. Later he invented an ingenious quick method to improve on it, and obtained π ≈ 3.1416 with only a 96-gon, with an accuracy comparable to that from a 1536-gon. His most important contribution in this area was his simple iterative π algorithm.

## Area of a circle

Liu Hui argued:

Multiply one side of a hexagon by the radius (of its circumcircle), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the finer we cut, the smaller the loss with respect to the area of circle, thus with further cut after cut, the area of the resulting polygon will coincide and become one with the circle; there will be no loss Liu Hui's method of calculating the area of a circle.

Further, Liu Hui proved that the area of a circle is half of its circumference multiplied by its radius. He said:

Between a polygon and a circle, there is excess radius. Multiply the excess radius by a side of the polygon. The resulting area exceeds the boundary of the circle

In the diagram d = excess radius. Multiplying d by one side results in oblong ABCD which exceeds the boundary of the circle. If a side of the polygon is small (i.e. there is a very large number of sides), then the excess radius will be small, hence excess area will be small.

Multiply the side of a polygon by its radius, and the area doubles; hence multiply half the circumference by the radius to yield the area of circle. The area within a circle is equal to the radius multiplied by half the circumference, or A = r x C/2 = r x r x π.

## Iterative algorithm

Liu Hui began with an inscribed hexagon. Let M be the length of one side AB of hexagon, r is the radius of circle. Bisect AB with line OPC, AC becomes one side of dodecagon (12-gon), let its length be m. Let the length of PC be j and the length of OP be G.

AOP, APC are two right angle triangles. Liu Hui used the Gou Gu (Pythagorean theorem) theorem repetitively:       From here, there is now a technique to determine m from M, which gives the side length for a polygon with twice the number of edges. Starting with a hexagon, Liu Hui could determine the side length of a dodecagon using this formula. Then continue repetitively to determine the side length of a 24-gon given the side length of a dodecagon. He could do this recursively as many times as necessary. Knowing how to determine the area of these polygons, Liu Hui could then approximate π.

## References

The Original Article can be found on https://github.com

#javascript #algorithms #datastructures #math

## Buddha Community  1620466520

If you accumulate data on which you base your decision-making as an organization, you should probably think about your data architecture and possible best practices.

If you accumulate data on which you base your decision-making as an organization, you most probably need to think about your data architecture and consider possible best practices. Gaining a competitive edge, remaining customer-centric to the greatest extent possible, and streamlining processes to get on-the-button outcomes can all be traced back to an organization’s capacity to build a future-ready data architecture.

In what follows, we offer a short overview of the overarching capabilities of data architecture. These include user-centricity, elasticity, robustness, and the capacity to ensure the seamless flow of data at all times. Added to these are automation enablement, plus security and data governance considerations. These points from our checklist for what we perceive to be an anticipatory analytics ecosystem.

#big data #data science #big data analytics #data analysis #data architecture #data transformation #data platform #data strategy #cloud data platform #data acquisition 1628881800

## JavaScript Algorithms and Data Structures: Math - Liu Hui π Algorithm

Liu Hui remarked in his commentary to The Nine Chapters on the Mathematical Art, that the ratio of the circumference of an inscribed hexagon to the diameter of the circle was three, hence π must be greater than three. He went on to provide a detailed step-by-step description of an iterative algorithm to calculate π to any required accuracy based on bisecting polygons; he calculated π to between 3.141024 and 3.142708 with a 96-gon; he suggested that 3.14 was a good enough approximation, and expressed π as 157/50; he admitted that this number was a bit small. Later he invented an ingenious quick method to improve on it, and obtained π ≈ 3.1416 with only a 96-gon, with an accuracy comparable to that from a 1536-gon. His most important contribution in this area was his simple iterative π algorithm.

## Area of a circle

Liu Hui argued:

Multiply one side of a hexagon by the radius (of its circumcircle), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the finer we cut, the smaller the loss with respect to the area of circle, thus with further cut after cut, the area of the resulting polygon will coincide and become one with the circle; there will be no loss Liu Hui's method of calculating the area of a circle.

Further, Liu Hui proved that the area of a circle is half of its circumference multiplied by its radius. He said:

Between a polygon and a circle, there is excess radius. Multiply the excess radius by a side of the polygon. The resulting area exceeds the boundary of the circle

In the diagram d = excess radius. Multiplying d by one side results in oblong ABCD which exceeds the boundary of the circle. If a side of the polygon is small (i.e. there is a very large number of sides), then the excess radius will be small, hence excess area will be small.

Multiply the side of a polygon by its radius, and the area doubles; hence multiply half the circumference by the radius to yield the area of circle. The area within a circle is equal to the radius multiplied by half the circumference, or A = r x C/2 = r x r x π.

## Iterative algorithm

Liu Hui began with an inscribed hexagon. Let M be the length of one side AB of hexagon, r is the radius of circle. Bisect AB with line OPC, AC becomes one side of dodecagon (12-gon), let its length be m. Let the length of PC be j and the length of OP be G.

AOP, APC are two right angle triangles. Liu Hui used the Gou Gu (Pythagorean theorem) theorem repetitively:       From here, there is now a technique to determine m from M, which gives the side length for a polygon with twice the number of edges. Starting with a hexagon, Liu Hui could determine the side length of a dodecagon using this formula. Then continue repetitively to determine the side length of a 24-gon given the side length of a dodecagon. He could do this recursively as many times as necessary. Knowing how to determine the area of these polygons, Liu Hui could then approximate π.

## References

The Original Article can be found on https://github.com

#javascript #algorithms #datastructures #math 1620629020

## Getting Started With Data Lakes

### Frameworks for Efficient Enterprise Analytics

The opportunities big data offers also come with very real challenges that many organizations are facing today. Often, it’s finding the most cost-effective, scalable way to store and process boundless volumes of data in multiple formats that come from a growing number of sources. Then organizations need the analytical capabilities and flexibility to turn this data into insights that can meet their specific business objectives.

This Refcard dives into how a data lake helps tackle these challenges at both ends — from its enhanced architecture that’s designed for efficient data ingestion, storage, and management to its advanced analytics functionality and performance flexibility. You’ll also explore key benefits and common use cases.

### Introduction

As technology continues to evolve with new data sources, such as IoT sensors and social media churning out large volumes of data, there has never been a better time to discuss the possibilities and challenges of managing such data for varying analytical insights. In this Refcard, we dig deep into how data lakes solve the problem of storing and processing enormous amounts of data. While doing so, we also explore the benefits of data lakes, their use cases, and how they differ from data warehouses (DWHs).

#big data #data analytics #data analysis #business analytics #data warehouse #data storage #data lake #data lake architecture #data lake governance #data lake management 1621986060

## Basics of Data Structure Algorithms

If I ask you what is your morning routine, what will you answer? Let me answer it for you. You will wake up in the morning, freshen up, you’ll go for some exercise, come back, bath, have breakfast, and then you’ll get ready for the rest of your day.

If you observe closely these are a set of rules that you follow daily to get ready for your work or classes. If you skip even one step, you will not achieve your task, which is getting ready for the day.

These steps do not contain the details like, at what time you wake up or which toothpaste did you use or did you go for a walk or to the gym, or what did you have in your breakfast. But all they do contain are some basic fundamental steps that you need to execute to perform some task. This is a very basic example of algorithms. This is an algorithm for your everyday morning.

In this article, we will be learning algorithms, their characteristics, types of algorithms, and most important the complexity of algorithms.

#### What are Data Structure Algorithms?

Algorithms are a finite set of rules that must be followed for problem-solving operations. Algorithms are step-by-step guides to how the execution of a process or a program is done on a machine to get the expected output.

• Do not contain complete programs or details. They are just logical solutions to a problem.
• Algorithms are expressible in simple language or flowchart.

#### Characteristics of an Algorithm in Data Structure

No one would follow any written instructions to follow a daily morning routine. Similarly, you cannot follow anything available in writing and consider it as an algorithm. To consider some instructions as an algorithm, they must have some specific characteristics :

1. Input: An algorithm, if required, should have very well-defined inputs. An algorithm can have zero or more inputs.

2. Output: Every algorithm should have one or more very well-defined outputs. Without an output, the algorithm fails to give the result of the tasks performed.

3. Unambiguous: The algorithm should be unambiguous and it should not have any confusion under any circumstances. All the sentences and steps should be clear and must have only one meaning.

4. Finiteness: The steps in the algorithm must be finite and there should be no infinite loops or steps in the algorithm. In simple words, an algorithm should always end.

5. Effectiveness: An algorithm should be simple, practically possible, and easy to understand for all users. It should be executable upon the available resources and should not contain any kind of futuristic technology or imagination.

6. Language independent: An algorithm must be in plain language so that it can be easily implemented in any computer language and yet the output should be the same as expected.

#### Data flow of the Algorithm in Data Structure

1. Problem: To write a solution you need to first identify the problem. The problem can be an example of the real-world for which we need to create a set of instructions to solve it.

2. Algorithm: Design a step-by-step procedure for the above problem and this procedure, after satisfying all the characteristics mentioned above, is an algorithm.

3. Input: After creating the algorithm, we need to give the required input. There can be zero or more inputs in an algorithm.

4. Processing unit: The input is now forwarded to the processing unit and this processing unit will produce the desired result according to the algorithm.

5. Output: The desired or expected output of the program according to the algorithm.

#### Why do we need Data Structure Algorithm?

Suppose you want to cook chole ( or chickpeas) for lunch. Now you cannot just go to the kitchen and set utensils on gas and start cooking them. You must have soaked them for at least 12 hours before cooking, then chop desired vegetables and follow many steps after that to get the delicious taste, texture, and nutrition.

This is the need for algorithms. To get desired output, you need to follow some specific set of rules. These rules do not contain details like in the above example, which masala you are using or which salt you are using, or how many chickpeas you are soaking. But all these rules contain a basic step-by-step guide for best results.

We need algorithms for the following two reasons :

1. Performance: The result should be as expected. You can break the large problems into smaller problems and solve each one of them to get the desired result. This also shows that the problem is feasible.

2. Scalability: When you have a big problem or a similar kind of smaller problem, the algorithm should work and give the desired output for both problems. In our example, no matter how many people you have for lunch the same algorithm of cooking chickpeas will work every single time if followed correctly.

Let us try to write an algorithm for our lunch problem :

1. Soak chickpeas in the night so that they are ready till the next afternoon.

2. Chop some vegetables that you like.

3. Set up a utensil on gas and saute the chopped vegetables.

4. Add water and wait for boiling.

5. Add chickpeas and wait until you get the desired texture.

The real-world example that we just discussed is a very close example of the algorithm. You cannot just start with step 3 and start cooking. You will not get the desired result. To get the desired result, you need to follow the specific order of rules. Also, each instruction should be clear in an algorithm as we can see in the above example.

#algorithms in data structure #data structure algorithms #algorithms 1617959340

## 4 Tips To Become A Successful Entry-Level Data Analyst

Companies across every industry rely on big data to make strategic decisions about their business, which is why data analyst roles are constantly in demand. Even as we transition to more automated data collection systems, data analysts remain a crucial piece in the data puzzle. Not only do they build the systems that extract and organize data, but they also make sense of it –– identifying patterns, trends, and formulating actionable insights.

If you think that an entry-level data analyst role might be right for you, you might be wondering what to focus on in the first 90 days on the job. What skills should you have going in and what should you focus on developing in order to advance in this career path?

Let’s take a look at the most important things you need to know.

#data #data-analytics #data-science #data-analysis #big-data-analytics #data-privacy #data-structures #good-company