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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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

- Aug 2
- 1 min

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.

7,923 views0 comments

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 ...

9 views0 comments

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.

159 views0 comments

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?

902 views0 comments

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

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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...

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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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