Mathematical Reflections – Archive

2023 Issues

Mathematical Reflections - Issue 5 2023
Article #1

Chasing a Red Herring
by Titu Andreescu and Marian Tetiva

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Article #2

A New Method to Solve and Refine Algebraic Inequalities
by Mihaly Bencze and Marius Dragan

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Problem Column

The deadline for submissions is November 15, 2023

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Solutions

Coming soon

Additional Resources
Coming Soon!
Mathematical Reflections – Issue 4 2023
Article #1

On a Class of Functional Equations
by Titu Andreescu and Marian Tetiva

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Article #2

Projective plane, Extended Complex Plane
by Nguyễn Minh Hà

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Problem Column

The deadline for submissions is September 15, 2023

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Solutions

Solutions to Mathematical Reflections 3, 2023:

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Additional Resources
Now available in our bookstore!
Mathematical Reflections – Issue 3 2023
Article #1

A Triangle Ratio Theorem and its Generalization to Higher Dimensions
by Hari Rajesh

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Article #2

Newton’s Quadrilateral Theorem
by Waldemar Pompe

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Problem Column

The deadline for submissions is July 15, 2023

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Solutions

Solutions to Mathematical Reflections 2, 2023:

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Additional Resources
Now available in our bookstore!
Mathematical Reflections – Issue 2 2023
Article #1

On a Combinatorial Identity
by Virgil Domocos

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Article #2


by

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Problem Column

The deadline for submissions is May 15, 2023

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Solutions

Solutions to Mathematical Reflections 1, 2023:

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Additional Resources
Coming soon to the bookstore!
Mathematical Reflections – Issue 1 2023
Article #1

A Few Generalizations of the Euler’s Totient Function
by Suzy Manuela Prajea

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Article #2

Solutions for the Frobenius Number in Three Variables
by Srijan Sundar

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Problem Column

The deadline for submissions is March 15, 2023

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Solutions

Solutions to Mathematical Reflections 6, 2022:

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Additional Resources
2022 Issues

Mathematical Reflections – Issue 6 2022
Article #1

An Interesting Generator of Parabolic Systems of Coaxial Circles Using Apollonius’ Problem
by Tran Quang Hung and Truong Tuan Nghia

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Article #2

by

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Problem Column

The deadline for submissions is January 15, 2023

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Solutions

Solutions to Mathematical Reflections 5, 2022:

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Additional Resources
This is a must have book for the MR readers
Mathematical Reflections – Issue 5 2022
Article #1

Sperner’s Lemma and Brouwer’s Fixed Point
by Farzad Rashidi

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Article #2


by

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Problem Column

The deadline for submissions is November 15, 2022

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Solutions

Solutions to Mathematical Reflections 4, 2022:

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Additional Resources
This is a great book for the MR readers
Mathematical Reflections – Issue 4 2022
Article #1

Local Monotony and Continuity
by Suzy Manuela Prajea

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Article #2

Formulas for Diagonals of any Quadrilateral
by Hayk Sedrakyan, Aidan Mozayeni

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Problem Column

The deadline for submissions is September 15, 2022

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Solutions

Solutions to Mathematical Reflections 3, 2022:

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Additional Resources
Any student interested in mathematics would cherish and enjoy this unique collection of meaningful problems and solutions.
Mathematical Reflections – Issue 3 2022
Article #1

The Missing Dominant Terms in a Fourier Series
by C. S. Jog

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Article #2

Solving Functional Equations in R+ Using Inequalities and Sequences
by Mohammad Hossein Rezaei

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Problem Column

The deadline for submissions is July 15, 2022

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Solutions

Solutions to Mathematical Reflections 2, 2022:

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Additional Resources
Any student interested in mathematics would cherish and enjoy this unique collection of meaningful problems and solutions.
Mathematical Reflections – Issue 2 2022
Article #1

Three Reflections
by Waldemar Pompe

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Article #2

A New Approach to the Interior Goat and Bird Problems
by C. S. Jog

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Problem Column

The deadline for submissions is May 15, 2022

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Solutions

Solutions to Mathematical Reflections 1, 2022:

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Additional Resources
Two new books are great resources for students who need to practice for the summer program admission test or for math enthusiasts to work on their problem solving skills.
Mathematical Reflections – Issue 1 2022
Article #1

Concurrency, Coliniarity, and Cyclicity using Homotheties
by Dr. Suzy Manuela Prajea

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Article #2

More on an Extension of Fagnano’s Problem
by Nguyen Minh Ha

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Problem Column

The deadline for submissions is March 15, 2022

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Solutions

Solutions to Mathematical Reflections 6, 2021:

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Additional Resources
Two new books are great resources for students who need to practice for the summer program admission test or for math enthusiasts to work on their problem solving skills.
2021 Issues

Mathematical Reflections – Issue 6 2021
Article #1

Tangential Quadrilaterals and Cyclicity
by Dr. Suzy Manuela Prajea

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Article #2


by

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Problem Column

The deadline for submissions is January 15, 2022

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Solutions

Solutions to Mathematical Reflections 5, 2021:

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Additional Resources
Two new books coming up soon! Great resources for students who need to practice for the summer program admission test or for math enthusiasts to work on their problem solving skills.
Mathematical Reflections – Issue 5 2021
Article #1

On the Relationship Between Inversive Geometry and the Cardinalities of Infinite Sets
by Akshaya Chakravarthy

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Article #2


by

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Problem Column

The deadline for submissions is November 15, 2021

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Solutions

Solutions to Mathematical Reflections 4, 2021:

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Additional Resources
Now available in our bookstore!
Mathematical Reflections – Issue 4 2021
Article #1

Midpoint of Symmedian Chord
by Srijon Sarkar

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Article #2


by

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Problem Column

The deadline for submissions is September 15, 2021

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Solutions

Solutions to Mathematical Reflections 3, 2021:

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Additional Resources
This is a great book for the MR readers
Mathematical Reflections – Issue 3 2021
Article #1

Cubic Polynomials Revisited
by Maitreyo Bhattacharjee

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Article #2


by

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Problem Column

The deadline for submissions is July 15, 2021

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Solutions

Solutions to Mathematical Reflections 2, 2021:

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Additional Resources
If you want to learn more about polynomials…
Mathematical Reflections – Issue 2 2021
Article #1

Additive Functions on Domains
by Navid Safaei

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Article #2


by

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Problem Column

The deadline for submissions is May 15, 2021

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Solutions

Solutions to Mathematical Reflections 1, 2021:

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Additional Resources
Learn more about Functional Equations from…
Mathematical Reflections – Issue 1 2021
Article #1

A Tetrahedron Whose Faces Have Equal Area Is “Equifacial”
by Titu Andreescu and Marian Tetiva

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Article #2


by

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Problem Column

The deadline for submissions is March 15, 2021

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Solutions

Solutions to Mathematical Reflections 6, 2020:

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Additional Resources
Discover natural mathematical vistas…
2020 Issues

Mathematical Reflections – Issue 6 2020
Article #1

Anti-Steiner Point Revisited
by Nguyen Duc Toan

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Article #2

Triangle BIC
by Shuborno Das, Aditya Khurmi, Aatman Supkar, Arindam Bhattacharyya

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Problem Column

The deadline for submissions is January 15, 2021

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Solutions

Solutions to Mathematical Reflections 5, 2020:

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Additional Resources
Learn more geometry from…
Mathematical Reflections – Issue 5 2020
Article #1

Counting with the Aid of Cyclotomic Polynomials
by İlker Can Çiçek

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Article #2

by

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Problem Column

The deadline for submissions is November 15, 2020

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Solutions

Solutions to Mathematical Reflections 4, 2020:

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Additional Resources
Learn more about polynomials…
Mathematical Reflections – Issue 4 2020
Article #1

Solving Problems by Looking at a Discriminant
by Jose Hernandez Santiago

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Article #2

The Continuous Solutions of Cauchy’s Functional Equation Using a Simple Geometric Argument
by Martin Celli

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Problem Column

The deadline for submissions is September 15, 2020

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Solutions

Solutions to Mathematical Reflections 3, 2020:

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Mathematical Reflections – Issue 3 2020
Article #1

Polar Duality in Olympiad Geometry
by Radek Olšák

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Article #2

Short Introduction to Deep Learning and its Math – Part II
by Branislav Kisacanin

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Problem Column

The deadline for submissions is July 15, 2020

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Solutions

Solutions to Mathematical Reflections 2, 2020:

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Mathematical Reflections – Issue 2 2020
Article #1

On Mixtilinear Incircles
by Jafet Baca

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Article #2

Short Introduction to Deep Learning and its Math
by Branislav Kisacanin

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Problem Column

The deadline for submissions is May 15, 2020

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Solutions

Solutions to Mathematical Reflections 1, 2020:

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Mathematical Reflections – Issue 1 2020
Article #1

A Geometric Interpretation of Some Polynomial Equations
by Navid Safaei

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Article #2

by

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Problem Column

The deadline for submissions is March 15, 2020

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Solutions

Solutions to Mathematical Reflections 6, 2019:

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2019 Issues

Mathematical Reflections – Issue 6 2019
Article #1

Ptolemy’s Sine Lemma
by Fedir Yudin and Nikita Skybytskyi

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Article #2

by

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Problem Column

The deadline for submissions is January 15, 2020

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Solutions

Solutions to Mathematical Reflections 5, 2019:

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Mathematical Reflections – Issue 5 2019
Article #1

On a Property of the Primitive Roots of Unity Leading to the Evaluation of Ramanujan’s Sums
by Titu Andreescu and Marian Tetiva

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Article #2


by

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Problem Column

The deadline for submissions is November 15, 2019

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Solutions

Solutions to Mathematical Reflections 4, 2019:

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Mathematical Reflections – Issue 4 2019
Article #1

Best Polynomial Estimates in a Triangle
by Titu Andreescu and Oleg Mushkarov

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Article #2


by

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Problem Column

The deadline for submissions is September 15, 2019

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Solutions

Solutions to Mathematical Reflections 3, 2019:

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Mathematical Reflections – Issue 3 2019
Article #1

Joining the Incenter and Orthocenter Configurations: Properties Associated with a Tangential Quadrilateral
by Andrew Wu

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Article #2


by

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Problem Column

The deadline for submissions is July 15, 2019

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Solutions

Solutions to Mathematical Reflections 2, 2019:

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Mathematical Reflections – Issue 2 2019
Article #1

Linear Approximation Implies Unique Solution
by Titu Andreescu and Marian Tetiva

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Article #2

Discrete Approach to a Result Concerning a Contour Integral
by Navid Safaei

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Problem Column

The deadline for submissions is May 15, 2019

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Solutions

Solutions to Mathematical Reflections 1, 2019:

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Mathematical Reflections – Issue 1 2019
Article #1

On a Special Center of Spiral Similarity
by Jafet Baca

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Article #2


by

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Problem Column

The deadline for submissions is March 15, 2019

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Solutions

Solutions to Mathematical Reflections 6, 2018:

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