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Mathematical Reflections – Archive

2022 Issues

Issue 3 - 2022 - Current Issue

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

Coming soon

Additional Resources

Any student interested in mathematics would cherish and enjoy this unique collection of meaningful problems and solutions.

Issue 2 - 2022

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.

Issue 1 - 2022

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

Issue 6 - 2021

Mathematical Reflections – Issue 6 2021

Article #1

Tangential Quadrilaterals and Cyclicity
by Dr. Suzy Manuela Prajea

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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.

Issue 5 - 2021

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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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!

Issue 4 - 2021

Mathematical Reflections – Issue 4 2021

Article #1

Midpoint of Symmedian Chord
by Srijon Sarkar

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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

Issue 3 - 2021

Mathematical Reflections – Issue 3 2021

Article #1

Cubic Polynomials Revisited
by Maitreyo Bhattacharjee

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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…

Issue 2 - 2021

Mathematical Reflections – Issue 2 2021

Article #1

Additive Functions on Domains
by Navid Safaei

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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…

Issue 1 - 2021

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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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

Issue 6 - 2020

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…

Issue 5 - 2020

Mathematical Reflections – Issue 5 2020

Article #1

Counting with the Aid of Cyclotomic Polynomials
by İlker Can Çiçek

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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…

Issue 4 - 2020

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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Issue 3 - 2020

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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Issue 2 - 2020

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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Issue 1 - 2020

Mathematical Reflections – Issue 1 2020

Article #1

A Geometric Interpretation of Some Polynomial Equations
by Navid Safaei

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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

Issue 6 - 2019

Mathematical Reflections – Issue 6 2019

Article #1

Ptolemy’s Sine Lemma
by Fedir Yudin and Nikita Skybytskyi

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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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Issue 5 - 2019

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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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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Issue 4 - 2019

Mathematical Reflections – Issue 4 2019

Article #1

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

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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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Issue 3 - 2019

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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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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Issue 2 - 2019

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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Issue 1 - 2019

Mathematical Reflections – Issue 1 2019

Article #1

On a Special Center of Spiral Similarity
by Jafet Baca

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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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