The Best Calculator

  • Facebook
  • RSS
  • Twitter

Pascal’s Triangle and Your Calculator

Email, RSS Follow
Pin It

Pascal’s triangle, named for French philosopher and mathematician Blaise Pascal, is an array of binomial coefficients presented in a triangle form.

Rows of Pascal’s triangle are structured from the top row (0th row) with conventional numerators beginning with 1. Each adjacent row consists of staggered values comprised of the sum of the numbers directly above the value. As rows are constructed below the preceding row, values are applied left to right, with a blank value treated as zero (making the left and right-most values therefore always equal to the top row.

Pascals triange

Concepts of Pascal’s triangle have been known for centuries, through the work of multiple mathematicians, possibly dating back as early as the 2nd century BC. Pascal presented the earliest formal treatise devoted specifically to the triangle. In his “Treatise on Arithmetical Triangle” Pascal not only presented results based on the triangle’s properties, but also employed them for solving problems in probability theory.

The triangle’s values and formula determine coefficients for binomial expansions.

Applications for Pascal’s Triangle

With the structure provided and formulas for determining the values within the rows, the triangle can be utilized in multiple ways:

Combinations – the Pascal triangle calculator formula can be utilized to solve the equation of an n value of items referenced by k at a time (stated as n choose k). Taking this combination for the row and entry in the triangle will solve the equation.

Binomial expansion – the formula of expanding powers of binomials can be utilized to populate the values in Pascal’s triangle. If you have a binomial and need to raise the power to perhaps the third or fourth power, rather than performing the multiplications needed, use Pascal’s triangle as your binomial expansion calculator.

Mathematical use of Pascal’s triangle can yield many useful functions:

Probabilities – want to know the probability of getting a certain result from something as basic as a coin toss? Pascal’s triangle can be utilized to solve the instance of any certain result given x number of tosses.

Need to know how many ways you can organize a team into 8 players, given a roster of 10 athletes? Go to row 10 of the triangle, and in to the 8th position (again recalling that the first position is designated as position 0).

Pascal Triangle Calculator Functions

With the complexity and functional values of utilizing Pascal’s triangle, you might surmise that there are tools available to utilize the triangle effectively on a scientific or graphing calculator.

To be sure, such functionality has been included – once you know how to get there. In the case of many TI calculators, for example, these functions are located under the MATH menu, (selecting “PRB”).

Following the example as above for “n choose k”, enter the statement as “x nCr  0” (where x = the row to be addressed) and press enter. The statement equates to “x choose 0”. Remember that the first row in the triangle is row zero, and the first entry in any given row is “1”. Using this statement with varying values allows you to access the values in Pascal’s triangle for any given row or position.

This makes calculator functions very powerful, in that you need not construct all levels of the triangle to arrive at a solution – the values in the triangle can be accessed directly. A simple expression such as “30 nCr 6” can, therefore, produce the value in Pascal’s triangle row 30 position 6.

Utilizing the triangle provides a much more straight-forward method for determining coefficients through binomial expansion rather than utilizing the binomial theorem method.

Given the impression of simplicity in constructing Pascal’s triangle, the number of uses and properties are astounding, due to the many properties and multiple patterns of numbers that are represented.

Graphing Calculators Make It Easy

Performing calculations for the combinations and probabilities functions available through the use of Pascal’s triangle can be accomplished quickly and easily.

To illustrate: owners of the TI 83/84 family of calculators can simply enter the first expression in the equation (such as 3 for the number of coin tosses in a probabilities example), hit the MATH key, then take the PRB (probabilities) function, and option 3 (nCr) to resolve the problem.

Other calculators such as the Casio scientific family have similar solutions for utilizing Pascal’s triangle for solutions.

Need Help?

To get more details on solving equations and binomial expansion with a calculator, there are a number of gracious individuals who have produced extremely helpful videos on YouTube.

These offerings walk you step-by-step through entering the variables right down to the keys to press, with various types of problems provided for examples.

Bottom Line

Pascal’s triangle provides many valuable patterns and applications for solving mathematical problems. Applying those principles through the use of sophisticated scientific/graphing calculators makes the process much easier and less prone to errors.

 

Feature image via Medium

Email, RSS Follow
Pin It

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Subscribe via Email

AMORTISATION CALCULATOR

Principal
Interest Rate
Years
Taxes + Insurance
Principal + Interest
Taxes + Insurance
Monthly Payments

Recent Articles

Best graphing calculator

Which Is The Best Graphing Calculator On The Market

November 30, 2018 By Jane Hickton

Ti 83 calculator

Review Of TI 83 Calculator: Advanced Graphing Calculator

November 22, 2018 By Jane Hickton

graphing calculator ti-84

How To Use The Graphing Calculator TI-84: Expert Techniques

October 29, 2018 By Jane Hickton

ti nspire calculator online

The TI Nspire Calculator Online Guide: An Introduction

October 29, 2018 By Jane Hickton

Arc Length Calculator

Arc Length Calculator: Finding The Necessary Values

October 22, 2018 By Jane Hickton

HP Prime Graphing Calculator

An A+ Tool: Review Of The HP Prime Graphing Calculator

September 30, 2018 By Jane Hickton

Asymptote calculator

Asymptote Calculator For Android And Apple Users

September 30, 2018 By Jane Hickton

Casio Collection Databank LED Calculator Watch

7 Best Calculator Watches for the Nerd Inside

September 3, 2018 By Jane Hickton

Sigma calculator

What Is Sigma Value And The Best Sigma Calculator

August 30, 2018 By Jane Hickton

Linear regression calculator

Step By Step Tutorial For Linear Regression Calculator

August 30, 2018 By Jane Hickton

Related Articles

  • calculator and graph

    How To Use a Graphing Calculator

    Sep 30, 2019
  • Black calculator on top of coins

    Calculators 101: How To Find The Best Calculator For Every Budget

    Jul 15, 2019
  • Serious millennial couple paying bills online

    Convergence Calculator; How To Calculate Geometric Series?

    Jun 26, 2019
  • Young man writing on a book

    TI-82 Guide: Basics, Special Functions, And More

    Jun 26, 2019
  • Young girl facing the board

    Trapezoidal Rule Calculator: Applications, GeoGebra, And More

    Apr 1, 2019
  • Vertex calculator

    Vertex Calculator Of Parabola: Overview, Tips, And More

    Dec 28, 2018
  • Function Calculator

    Function Calculator With Steps: Overview, Benefits, And Drawbacks

    Dec 28, 2018
  • Ti 83 calculator

    Review Of TI 83 Calculator: Advanced Graphing Calculator

    Nov 22, 2018
  • HP Prime Graphing Calculator

    An A+ Tool: Review Of The HP Prime Graphing Calculator

    Sep 30, 2018
  • Casio Collection Databank LED Calculator Watch

    7 Best Calculator Watches for the Nerd Inside

    Sep 3, 2018

Copyright © 2021 TheBestCalculator.com

Privacy Policy · Terms of Use · Sitemap · Contact

This website uses cookies to ensure you get the best experience on our website. Learn more.