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.
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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.
Arif Erkoca
- Jan 18
- 1 min
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!
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Arif Erkoca
- Dec 5, 2022
- 1 min
Parabola and Parabolic Mirrors
The derivation of parabolic mirror equations (both for concave and convex mirrors) are presented. The relations between object and image ...
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Arif Erkoca
- Oct 5, 2022
- 1 min
Moving on a Grid (Probability Calculations)
Great problems on permutation with repetitions. We are finding the probabilities of paths taken on a grid structure.
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Arif Erkoca
- Jul 7, 2022
- 1 min
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.
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Arif Erkoca
- Jul 6, 2022
- 0 min
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.
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Arif Erkoca
- Dec 18, 2021
- 1 min
Which one is Bigger?
Which number is bigger, 100 to the power 101 or 101 to the power 100?
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Ashlar STEM
- May 21, 2021
- 2 min
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.
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Ashlar STEM
- Apr 16, 2021
- 1 min
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.
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Ashlar STEM
- Mar 5, 2021
- 1 min
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
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Ashlar STEM
- Feb 26, 2021
- 1 min
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.
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Ashlar STEM
- Feb 12, 2021
- 3 min
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?
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Ashlar STEM
- Feb 4, 2021
- 6 min
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?
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Ashlar STEM
- Jan 22, 2021
- 1 min
MINIMUM WHOLE NUMBER VALUE
ARITHMETIC MEAN vs GEOMETRIC MEAN Copyright © 2021 Ashlar STEM Academy
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Ashlar STEM
- Jan 15, 2021
- 1 min
An Interesting Geometry Problem
Finding the minimum of a function with multiple variables DOWNLOAD THE SOLUTION (PDF, 360KB) Copyright © 2021 Ashlar STEM Academy
180 views0 comments
Ashlar STEM
- Nov 14, 2020
- 1 min
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...
68 views0 comments
Ashlar STEM
- Aug 31, 2020
- 1 min
SMOOTH GOLDEN EGGS
In this paper, I demonstrate how to plot smooth “Golden Eggs” using mathematical functions.
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Ashlar STEM
- Mar 6, 2020
- 2 min
Converting Decimals to Binaries
We present how to convert both whole and fractional decimal numbers to their binary equivalents.
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Ashlar STEM
- Feb 22, 2020
- 1 min
What is 1 + 3 + 5 + 7 + ... 99 = ?
How to add numbers using geometry?
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Ashlar STEM
- Dec 29, 2019
- 1 min
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...
145 views0 comments
Ashlar STEM
- Dec 6, 2018
- 1 min
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...
25 views0 comments
Ashlar STEM
- Dec 3, 2018
- 1 min
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...
16 views0 comments
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