Wolfram|Alpha Examples: Mathematics (2024)

Examples for

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge. Get help with math homework, solve specific math problems or find information on mathematical subjects and topics.

Elementary Math

Do basic arithmetic. Work with fractions, percentages and similar fundamentals. Solve place value and word problems.

Do basic arithmetic:

125 + 375

Do exact arithmetic with fractions:

1/4 * (4 - 1/2)
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Geometry

Compute the properties of geometric objects of various kinds in 2, 3 or higher dimensions. Explore and apply ideas from many subfields of geometry.

Compute properties of a geometric figure:

annulus, inner radius=2, outer radius=5

Plot a conic section and identify its type:

2x^2 - 3xy + 4y^2 + 6x - 3y - 4 = 0

Compute properties of a polyhedron:

dodecahedron
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Numbers

Work with various kinds of numbers. Check for membership in larger sets, such as the rationals or the transcendental numbers. Convert between bases.

Compute a decimal approximation to a specified number of digits:

pi to 1000 digits

Convert a decimal number to another base:

219 to binary
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Number Theory

Analyze integers; subsets of the integers, including the prime numbers; and related ideas.

Compute a prime factorization:

factor 70560

Solve a Diophantine equation:

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Applied Mathematics

Perform numerical analysis and optimization of systems and objects, including packing and covering of objects and control systems.

Minimize or maximize a function:

maximize x(1-x)e^x

Numerically integrate functions that cannot be integrated symbolically:

integrate sin(cos x) from x=0 to 1
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Mathematical Definitions

Make queries about various definitions and descriptions in mathematics.

Find information about a math concept:

tangram

Get a brief definition:

basic definition of prime number
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Statistics

Compute properties of datasets, perform statistical inference or model data. Work with probability distributions and random variables.

Calculate basic descriptive statistics for a data set:

{25, 35, 10, 17, 29, 14, 21, 31}

Find the sample size needed to estimate a binomial parameter:

sample size for binomial parameter
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Algebra

Find roots of and expand, factor or simplify mathematical expressions—everything from polynomials to fields and groups.

Solve an equation:

x^3 - 4x^2 + 6x - 24 = 0

Factor a polynomial:

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48

Simplify an expression:

1/(1+sqrt(2))
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Differential Equations

Solve differential equations of any order. Examine solutions and plots of the solution families. Specify initial conditions to find exact solutions.

Solve a linear ordinary differential equation:

y'' + y = 0

Specify initial values:

y'' + y = 0, y(0)=2, y'(0)=1

Solve a nonlinear equation:

f'(t) = f(t)^2 + 1
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Trigonometry

Perform trigonometric calculations and explore properties of trigonometric functions and identities.

Compute values of trigonometric functions:

Solve a trigonometric equation:

sin x + cos x = 1
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Discrete Mathematics

Explore sequences and recurrences, solve common problems in combinatorics and compute properties of graphs and lattices.

Compute a possible formula and continuation for a sequence:

5, 14, 23, 32, 41, ...

Analyze a graph specified by adjacency rules:

1->2, 2->3, 3->1, 3->4, 4->1

Solve a recurrence:

f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2
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Evaluate Boolean logic expressions and expressions involving sets and set operators. Solve Boolean equations. Compute truth tables. Generate Venn diagrams.

Compute a truth table:

Generate a Venn diagram:

(complement S) intersect (A union B)
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Famous Math Problems

Gather information about famous problems, conjectures, theorems and paradoxes. Learn about them and their formulators.

Get information about a mathematical conjecture:

Riemann Hypothesis

Get historical information about a theorem:

Fermat's little theorem
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Probability

Compute the probabilities of certain events occurring. Compute joint, disjoint or conditional probabilities and apply them to real-world situations.

Compute the probability of a union of events:

probability of the union of three events

Compute coin‐toss probabilities:

32 coin tosses
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Compute integrals, derivatives and limits as well as analyze sums, products and series.

Compute an integral:

integrate sin x dx from x=0 to pi

Calculate a derivative:

derivative of x^4 sin x

Solve an ordinary differential equation:

y'' + y = 0
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Visualize functions, equations and inequalities. Do so in 1, 2 or 3 dimensions. Make polar and parametric plots.

Plot a function:

plot x^3 - 6x^2 + 4x + 12

Plot a region satisfying multiple inequalities:

plot x^2+y^2<1 and y>x
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Linear Algebra

Explore and compute properties of vectors, matrices and vector spaces.

Compute properties of a vector:

vector <3, -4>

Calculate properties of a matrix:

{{6, -7}, {0, 3}}

Determine whether a set of vectors is linearly independent:

Are (2, -1) and (4, 2) linearly independent?
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Complex Analysis

Analyze functions and expressions containing imaginary numbers or complex variables.

Compute properties of a function of a complex variable (use the variable z):

e^z

Compute the residue of a function at a point:

residue of 1/(z^2+4)^2 at z=2i
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Mathematical Functions

Examine the properties of mathematical functions, such as continuity, surjectivity and parity. Utilize notable special functions or number theoretic functions.

Do computations with special functions:

d/dx Si(x)^2

Do computations with number theoretic functions:

phi(110)

Find representations for a function:

gamma(x) integral representation
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Continued Fractions

Compute; learn about algorithms, definitions and theorems involving; or find properties of continued fractions.

Find the continued fraction representation of a number:

continued fraction pi

Find definitions of continued fraction terminology:

what is a regular continued fraction

Find continued fraction papers by author:

continued fraction papers by Stern
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Common Core Math

Get information about math Common Core Standards for kindergarten through eighth grade.

Evaluate an expression (CCSS.Math.Content.6.EE.A.2c):

if x = 4, what is 3x + 50?

Perform multiple operations with rational numbers (CCSS.Math.Content.7.NS.A.2c):

(-1/2 + 3/8 + 1/4 + -3/2) / 2
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Wolfram|Alpha Examples: Mathematics (2024)

FAQs

What is Wolfram Alpha's example? ›

Wolframalpha Examples. By now you might have heard about Wolfram|Alpha. It is an online computational engine which is a work in progress. It is useful for our classes for doing some quick data lookup, computations, plots, etc.

What is Wolfram used for in everyday life? ›

Look up Oscar winners, compute nutritional values for meals, keep tabs on your stock portfolio, check the weather or convert recipe measurements—Wolfram|Alpha's powerful algorithms and massive knowledgebase can help with everyday tasks from cooking to homework to changing a tire.

What is the rule of three Wolfram? ›

The so-called rule of three is an educational tool utilized historically to verbalize the process of solving basic linear equations with four terms where three of the terms are known. Evidence suggests that there are two "different" rules of three: One direct and one inverse.

Can Wolfram Alpha solve any math problem? ›

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge.

Does Wolfram Alpha make mistakes? ›

Usually, but not necessarily. Some results may depend on the time and/or location of the query. In addition, Wolfram|Alpha is continually being updated and enhanced.

Does ChatGPT use Wolfram Alpha? ›

But they have a common interface: natural language. And this means that ChatGPT can “talk to” Wolfram|Alpha just like humans do—with Wolfram|Alpha turning the natural language it gets from ChatGPT into precise, symbolic computational language on which it can apply its computational knowledge power.

What is Wolfram called now? ›

The names tungsten and wolfram have been used for the metal since its discovery, though everywhere Jön Jacob Berzelius's symbol W prevails. In British and American usage, tungsten is preferred; in Germany and a number of other European countries, wolfram is accepted.

Which element is known as Wolfram? ›

Tungsten (also called wolfram) is a chemical element; it has symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively as compounds with other elements. It was identified as a new element in 1781 and first isolated as a metal in 1783.

Why is it called Wolfram? ›

However, it seems unlikely to me that such a colourful name as wolfram will be forgotten. In case you were wondering, it is believed to be derived from the German for 'wolf's foam'.

What is the Benford's law of Wolfram? ›

Benford's law states that for base , the probability that the first digit of numbers in many classes of real-world datasets is 1 is not given by 1/9 ≈ 11.1% (as would be naively expected) but is actually closer to 30%.

What is rule 30 wolfram? ›

Rule 30 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its color and its immediate neighbors. Its rule outcomes are encoded in the binary representation. .

What is the 4 rule in math? ›

The Rule of Four stipulates that topics in mathematics should be presented in four ways: geometrically, numerically, analytically, and verbally. Implementing the Rule of Four supports students in being adept with all four types of representations and also provides support to students who learn in different ways.

What does e mean in math? ›

The term “Euler's number (e)” refers to a mathematical expression for the base of the natural logarithm. This is represented by a non-repeating number that never ends. The first few digits of Euler's number are 2.71828.

Can Wolfram solve physics? ›

Wolfram|Alpha helps you explore step-by-step answers to a wide range of physics problems to help with homework or general education. Use flexible formulas to solve different variables for the same equation with topics covering the full range of physics, including electromagnetism, relativity and Newtonian mechanics.

Can Wolfram do word problems? ›

Because the Wolfram Language has powerful symbolic computation ability, Wolfram|Alpha can interpret basic mathematical word problems and give descriptive results.

What do people use Wolfram Alpha for? ›

WolframAlpha (/ˈwʊlf. rəm-/ WUULf-rəm-) is an answer engine developed by Wolfram Research. It is offered as an online service that answers factual queries by computing answers from externally sourced data.

Is Wolfram Alpha an example of a search tool? ›

Expert-Verified Answer

It is true to say that Wolfram Alpha is an example of a search tool that can help us solve factual questions to help complete my homework. Wolfram Alpha was delivered on May 18, 2009 and depends on Wolfram's prior item Wolfram Mathematica, a specialized figuring platform.

What is the meaning of Wolfram Alpha? ›

Wolfram Alpha defines itself as a “computational knowledge engine,” a computer-based knowledge machine. The answer to the alignment is already given. This semantic search engine wants to provide specific results on queries since 2005.

What are the applications of Wolfram Alpha? ›

These include:
  • Artificial Intelligence (AI)
  • Computational Knowledge.
  • Natural Language Processing (NLP)
  • Data Analytics.
  • Decision Support Systems.
Dec 23, 2023

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