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MATH
BLOG
Some think mathematics is only an abstract notion. Here in this BLOG, we not only present its pure beauty, but also its existence in Nature.
Birthdays of N People in a Room
There are N randomly chosen people in a room. Let Q(N) be the probability of having all these N people to have different birthdays ...
Ashlar STEM
Jan 31 min read
How to Solve Cubic Equations
Learn how to solve cubic equations using the cubic formula, which is derived in this paper. Trigonometric substitution method is presented.
Arif Erkoca
Aug 2, 20231 min read
How to Slice an Elliptical Pizza?
A pizzeria serves elliptical pizzas. We need to figure out how to cut it into equal size slices to feed 8 people. A great Calculus question!
Arif Erkoca
Jan 18, 20231 min read
Parabola and Parabolic Mirrors
The derivation of parabolic mirror equations (both for concave and convex mirrors) are presented. The relations between object and image ...
Arif Erkoca
Dec 5, 20221 min read
Moving on a Grid (Probability Calculations)
Great problems on permutation with repetitions. We are finding the probabilities of paths taken on a grid structure.
Arif Erkoca
Oct 5, 20221 min read
arctan(1) + arctan(2) + arctan(3) = ?
Trigonometric functions are vastly used in many different areas, and so are inverse trigonometric ones. This question is about the latter.
Arif Erkoca
Jul 7, 20221 min read
Sum of Cubes of n Natural Numbers
Closed form for the sum of cubes of n natural numbers is derived here. An interesting identity is given at the end.
Arif Erkoca
Jul 6, 20220 min read
Which one is Bigger?
Which number is bigger, 100 to the power 101 or 101 to the power 100?
Arif Erkoca
Dec 18, 20211 min read
Do we really need a calculator to find the sine of 1 degree?
We give a highly accurate and precise estimate for the value of sine 1 degree. All is done by just using basic four operations.
Ashlar STEM
May 21, 20212 min read
How to Solve Cubic Equations
In this review article, we present the derivation of the quadratic and cubic formulae by using the geometrical symmetries in each case.
Ashlar STEM
Apr 16, 20211 min read
Numbers Around a Circle
There are 201 numbers distributed around a circle such that the sum of 18 consecutive numbers is 12. Find the numbers based on the fact that
Ashlar STEM
Mar 5, 20211 min read
Mathematical Shape of a Hanging Cable from Two Poles
Shape of a Hanging Cable from Two Poles is determined here. This is the famous catenary problem in Physics.
Ashlar STEM
Feb 26, 20211 min read
Probability of seeing your friend
Two friends are meeting at a coffee shop. If they can see each other there with 50% probability, for how long does each one need to wait?
Ashlar STEM
Feb 12, 20213 min read
Probability to form a Triangle by breaking a Rod
A rod with length L is broken into three pieces. Can you find the probability for forming a triangle out of these three pieces?
Ashlar STEM
Feb 4, 20216 min read
MINIMUM WHOLE NUMBER VALUE
ARITHMETIC MEAN vs GEOMETRIC MEAN
Ashlar STEM
Jan 22, 20211 min read
An Interesting Geometry Problem
Finding the minimum of a function with multiple variables
Ashlar STEM
Jan 15, 20211 min read
Counting The Number of Ways
It is always a daunting task for most studying probability or mathematical statistics to figure out the number of ways a selection can be...
Ashlar STEM
Nov 14, 20201 min read
SMOOTH GOLDEN EGGS
In this paper, I demonstrate how to plot smooth “Golden Eggs” using mathematical functions.
Ashlar STEM
Aug 31, 20201 min read
Converting Decimals to Binaries
We present how to convert both whole and fractional decimal numbers to their binary equivalents.
Ashlar STEM
Mar 6, 20202 min read
What is 1 + 3 + 5 + 7 + ... 99 = ?
How to add numbers using geometry?
Ashlar STEM
Feb 22, 20201 min read
4 Gallons of Water PUZZLE!
Suppose you were given one three-gallon-bucket and one five-gallon-bucket. There is also a water tap available for you to fill these...
Ashlar STEM
Dec 29, 20191 min read
What are the two numbers?
One day I run into two of my friends from university, Rosalind and Max. We immediately started to talk about science and math as we used...
Ashlar STEM
Dec 6, 20181 min read
Why do we use base 10 number system?
Starting our elementary school years, we all learn how to do arithmetic using the number system of base 10. All basic operations are...
Ashlar STEM
Dec 3, 20181 min read
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