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Minimal cost
A power house, P, is on one bank of a straight river W meters wide, and a factory, F, is on the opposite bank L meters downstrea...

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Euclidean distance from a point to a polynomial
A not uncommon problem in the area of computational geometry is to find the closest point to a straight line from a given point,...

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Fun with a compass
Each night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometr...

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Is It a Snake?
Given an m-by-n matrix, return true if the elements of the matrix are a connected "snake" shape from 1 to m*n. Otherwise return ...

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Convex Hull Capture
Imagine four points in uv that form a square. uv = [ ... 0,0; 0,2; 2,2; 2,0]; Now we have two more po...

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solid of revolution
Given an real polynomial P and two real numbers a,b with 0<=a<=b. Calculate the volume of the solid of revolution made by rotati...

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Find the Area of a Polygon
Consider 2-D geometry and assume that the points are given in form of rows of a matrix. Find the area of polygon enclosed by the...

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Angle bisectors
Given 2 direction vectors, calculate the *_two_ (2) normalized angle bisectors* (which are perpendicular between them). Input...

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Regular polygon bounded by and bounding a circle
As the number of sides (or vertices) of a regular polygon goes to infinity, its perimeter and area go to the perimeter and area ...

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Radiation Heat Transfer — View Factors (5)
View factors (aka configuration factors) are utilized in some radiation heat transfer models to estimate heat transfer rates bet...

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Find the sines of an isosceles triangle when given its area and height
Find the sines of an isosceles triangle when given its area and height. For example, when A=12 and h=4, the result is [0.8 0.8 ...

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Under the sea: Snell's law & total internal reflection
<https://en.wikipedia.org/wiki/Snell's_law> When a light travels from one medium to another medium, depending on the refracti...

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Radiation Heat Transfer — View Factors (4)
View factors (aka configuration factors) are utilized in some radiation heat transfer models to estimate heat transfer rates bet...

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Easy Sequences 21: Combinatorial Summations
Create the function S(n), defined by the following summation: The symbol is the combination f...

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Easy Sequences 27: Product of Radicals of Integers
The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

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Easy Sequences 5: Project Euler Problem 1 - Again!
We are all familiar with Project Euler Problem 1. This time let's try it on bigger multiples and larger range. Find the sum of ...

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Easy Sequences 11: Factorial Digits without Trailing Zeros
Here is an easy one... It is not difficult to count the number of digits of the factorial of a given number. For example for 'n...

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Easy Sequences 6: Coefficient sums of derivatives
Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respecti...

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Easy Sequences 3: Prime 44-number Squares
The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd ...

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Easy Sequences 4: Eliminate the Days of Confusion
If a date is written in purely numeric format some dates can be confusing, if we don't know the date format used. For example, "...

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Easy Sequences 9: Faithful Pairs
A "faithful number" is a non-prime number that is one less or one more than some prime number but not both. For example, for num...

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Easy Sequences 10: Sum of Cumsums of Fibonacci Sequence
The function F(n) is defined as the set of Fibonacci numbers from the first up to the n-th. S(n) is the result of applying to F,...

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Easy Sequences 1: Find the index of an element
The nth element of a series is defined by: . Obviously, the first element . Given the nth element , find the value of the corre...

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Easy Sequences 42: Areas of Non-constructible Polygons
A constructible polygon is a regular polygon that can be constructed using only a compass and a straightedge. Amazingly, Gauss ...

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Easy Sequences 41: Boxes with Integer Edges
For this problem, we are asked to write a function that will count the number of boxes with integer edges, that has the same giv...

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Easy Sequences 44: Finding the Smallest Number whose Cube is divisible by a Factorial
Given a integer , our goal is to find the smallest integer , such that divides . For example, for , , because , (since ), and ...

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Easy Sequences 38: Prime Number Delta
The Prime Number Theorem states that: where is the prime counting function (number of pri...

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Splitting Hexagon - Problem the third

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Splitting Circle
Consider a circle which has been divided into three concentric circles as depicted in the figure below The ratio betwen the a...

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Splitting Square - Problem the first

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