University of Toronto Mathematics Network

Question Corner and Discussion Area

Unfortunately, due to limited resources we have been unable to make staff available to continue providing this service, though we hope to be able to provide it again in the future.

However, please browse the large selection of questions and answers already posted; you will likely find your question addressed there somewhere.

Question Topics

Questions Arranged Roughly By Subject

• An Infinitely Recurring Square Root
• Finding the Sum of a Power Series
• The Sum of the Geometric Series 1 + 1/2 + 1/4 + ...
• A Complicated-Looking Infinite Sum
• A Geometric Series Arising From an Arithmetic Series
• Finding the Ratio from the Sum of a Geometric Series
• Numbers Defined By Infinite Sums
• A Sequence Describing a Bouncing Ball

Geometry-General

• Angle Between Vertices of a Tetrahedron
• Counting Obtuse Triangles in an Inscribed Polygon
• Fractals and their History
• Four-dimensional Pyramids

Geometry-Euclidean and Non-Euclidean

• Euclidean Geometry
• Euclidean Geometry in Higher Dimensions
• Non-Euclidean Geometry
• Understanding Projective Geometry
• Vectors in Projective Geometry
• Do Parallel Lines Meet At Infinity?

Geometry-Constructions and Proofs

• Constructing a Pentagon
• The Three Classical Impossible Constructions of Geometry
• Using Geometric Postulates for Theorems in 3 Dimensions
• Counting Points and Lines Using Axioms
• Deductive and Inductive Reasoning

Geometry-Basic Concepts

• Questions about Slopes and Lines
• Why The Midpoint Formula Works
• Infinity, Pi and Symmetry

Complex Numbers

• Why is e^(pi i) = -1?
• What is the Square Root of i?
• What is i to the Power of i?
• Raising a Number to a Complex Power
• The Origin of Complex Numbers and the Notation "i"
• Complex Numbers in Real Life
• More Complex Number Questions
• Geometry and Imaginary Numbers

Recreational Mathematics and Mathematics in Music

• Patterns in the Towers of Hanoi Solution
• Musical Frequencies and Other Questions
• The Mathematics of Drum Design

Algebra and Calculus

• Multiplying Matrices
• How To Graph The Inverse Of A Function
• Does Every Function Have an Antiderivative?
• Symmetry of Functions and their Derivatives
• Factorials of Non-Integral Values

Polynomial and Transcendental Equations

• Solution to the Transcendental Equation 2^x + 3^x = 5
• Limit of the Sequence a(n) = cos(a(n-1))
• Solving a Quadratic with Non-Constant Coefficients
• Solution to a Functional Equation

Number Systems and Number Theory

• Largest Possible Number?
• Calculating Digits of Pi in Other Bases
• Tetrahedral and 4-Tetrahedral Numbers
• Existence of Shapes with Irrational Dimensions
• What are the Origins of Number Systems?
• The Hypercomplex Numbers
• Why is the Product of Negative Numbers Positive?
• The Number Zero
• Why You Can't Divide Nine By Zero
• Why is x^0 = 1?
• How To Express A Repeating Decimal Number As A Fraction
• Published Proof of Fermat's Last Theorem
• The n=4 Case of Fermat's Last Theorem
• The Case n=3 Of Fermat's Last Theorem
• A Question from the IMO
• How To Find The Least Common Multiple
• A Geometric Proof That The Square Root Of Two Is Irrational

Historical Questions

• Which U.S. President Re-Proved the Pythagorean Theorem?
• Why Arithmetic and Geometric Sequences are Called What They Are
• Origin of the Notation for Slope
• Why We Use "Argument" In Describing Complex Angles
• The Origin Of The Word Quadratic
• The Origin Of Geometry
• Origin of Orders of Operations

Practical Questions

• How To Code Information With Error Detection
• How To Build A Parabolic Dish
• How To Compute Standings In Baseball
• Regular Withdrawals on Compound Interest
• Applications of the Geometric Mean
• Scientific Notation in Everyday Life
• Natural Logs in the Real World
• Use of Neural Networks for Empirical Data
• Calculating Square Roots
• How to Draw a Circle on a Computer
• Finding the Focus of a Parabolic Dish
• The Decomposition of a Drug in the Human Body
• Calculating Angles In A Pyramid
• Applications of Polynomial Factorization

Probability Theory

• Interpreting the "Expected Number"

Miscellaneous

• What are Antiatoms Made Of?
• The Four Fours Problem
• Generalizing the Towers of Hanoi Problem

Ask Your Own Question

• Ask Your Own Question

Discussion Topics

• Is Deductive Geometry Worth Salvaging in the High-School Curriculum?
• Anyone Have Interesting Graphing Calculator Problems?
• How Much Does School Size affect Performance in Math Contests?
• Starting a Math Club
• Mathematical Communication
• Teaching Linear Equations With CDROM Technology
• Teaching Addition Using Fractions and Decimals Together
• Success in Mathematics and Future Success
• Student Misconceptions about Complex Numbers
• Motivating Students

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