Compass and straightedge constructions | Cubic irrational numbers | History of geometry | Unsolvable puzzles | Euclidean plane geometry
Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible to construct by using only a compass and straightedge, but even in ancient times solutions were known that employed other tools. The Egyptians, Indians, and particularly the Greeks were aware of the problem and made many futile attempts at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a compass-and-straightedge solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x3 = 2; in other words, x = , the cube root of two. This is because a cube of side length 1 has a volume of 13 = 1, and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that is not a constructible number. This is a consequence of the fact that the coordinates of a new point constructed by a compass and straightedge are roots of polynomials over the field generated by the coordinates of previous points, of no greater degree than a quadratic. This implies that the degree of the field extension generated by a constructible point must be a power of 2. The field extension generated by , however, is of degree 3. (Wikipedia).
Lesson: Factoring a Sum or Difference of Cubes
This video verifies for factoring formulas and provides examples on how to factor a sum or difference of cubes. http://mathispower4u.com
From playlist Factoring a Sum or Difference of Cubes
How to take the odd root of a negative integer, cube root
👉 Learn how to find the cube root of a number. To find the cube root of a number, we identify whether that number which we want to find its cube root is a perfect cube. This is done by identifying a number which when raised to the 3rd power gives the number which we want to find its cube r
From playlist How To Simplify The Cube Root of a Number
(New Version Available) Factoring a Sum or Difference of Cubes
New Version: https://youtu.be/pRgiZ9pLnOc The video explains how to fact polynomials in the form a^3 + b^3 and a^3 + b^3. http://mathispower4u.wordpress.com/
From playlist Factoring a Sum or Difference of Cubes
Puzzle video: http://www.youtube.com/watch?v=wTsoUJKpbs8 Next puzzle: http://www.youtube.com/watch?v=RJ-iiF81TxE Music by Bertrand Laurence http://www.bertrandlaurence.com used with permission. Find me on FaceBook: https://www.facebook.com/YouTubeTyYann
From playlist Tricks and Math Puzzles answers
Using prime factorization to take the cube root of a number, cuberoot(64)
👉 Learn how to find the cube root of a number. To find the cube root of a number, we identify whether that number which we want to find its cube root is a perfect cube. This is done by identifying a number which when raised to the 3rd power gives the number which we want to find its cube r
From playlist How To Simplify The Cube Root of a Number
Next Puzzle: http://www.youtube.com/watch?v=RJ-iiF81TxE Previous Puzzle: http://www.youtube.com/watch?v=jDjWMQRt6WM Solution: http://www.youtube.com/watch?v=j2_BRoQAInY Music by Bertrand Laurence http://www.bertrandlaurence.com used with permission. Find me on FaceBook: https://www.faceboo
From playlist Tricks and Math Puzzles
Related Rates The Surface Area of a Cube
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Related Rates The Surface Area of a Cube. All edges of a cube are expanding at a rate of 5 centimeters per second. How fast is the surface area changing when each edge is 3 centimeters?
From playlist Calculus
Calculus Limit with Difference of Cubes Formula
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Calculus Limit with Difference of Cubes Formula
From playlist Calculus
Difference of Two Cubes - Practice 3
Another practice set with the difference of two cubes
From playlist Algebra
Reduction of Order -- Differential Equations Examples #13
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From playlist Differential Equations
4th dimension 'n stuff -- Day 3
alright, got the structure for everything in. We'll see how this goes! -- Watch live at https://www.twitch.tv/simuleios
From playlist 4d visualization
2000 years unsolved: Why is doubling cubes and squaring circles impossible?
Today's video is about the resolution of four problems that remained open for over 2000 years from when they were first puzzled over in ancient Greece: Is it possible, just using an ideal mathematical ruler and an ideal mathematical compass, to double cubes, trisect angles, construct regul
From playlist Recent videos
Factoring Polynomials Completely - All Types (100 Problems & Free Worksheet)
Learn how to factor polynomials completely in this video math tutorial by Mario's Math Tutoring. We will be going through 100 factoring problems including greatest common factor, difference of 2 squares, sum and difference of 2 cubes, perfect square trinomials, trinomials with leading coe
From playlist Factoring - All Different Types
Factorisation by Algebraic Long Division | Revision for Maths A-Level or IB
I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. A-Level Maths Courses, FREE revision guide and wor
From playlist A-Level Maths | Revision Playlist
Calculus 15.4 Applications of Double Integrals
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
GCSE Maths: Volume of 3D Shapes Livestream
The third of six livestreams happening every Friday at 4pm (GMT +1) discussing the topics of the Tom Rocks Maths Appeal GCSE Maths series. The topic this week is the Volume of 3D shapes (Cubes, Cuboids, Prisms and Cylinders) - full list of questions discussed (with timestamps) below. How
From playlist Tom Rocks GCSE Maths Appeal
The Factor Theorem | Algebra | GCSE Further Maths | A-Level Maths Series
A video revising the techniques and strategies for working with the factor theorem (GCSE Further Maths & A-Level Only). This video is part of the Algebra module in GCSE Further Maths & A-Level maths, see my other videos below to continue with the series. 👑 Everything you Need to Pass you
From playlist A-Level Maths Series - Pure Mathematics
Area Between Curves | Integration | Revision for Maths A-Level and IB
I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. Tutoring - We can match you with an experienced t
From playlist A-Level Maths | Revision Playlist
Evaluate a Double Integral over a Trapezoidal Region Requiring Integration by Part
This video explains how to set-up and evaluate a double integral over a trapezoidal region.
From playlist Double Integrals
Take the cube root of a number using the product of cubed numbers, cuberoot(250)
👉 Learn how to find the cube root of a number. To find the cube root of a number, we identify whether that number which we want to find its cube root is a perfect cube. This is done by identifying a number which when raised to the 3rd power gives the number which we want to find its cube r
From playlist How To Simplify The Cube Root of a Number