How to interpret 3^3 + 4^3 + 5^3 = 6^3 ?

  • Context: Undergrad 
  • Thread starter Thread starter josdavi
  • Start date Start date
Click For Summary
SUMMARY

The equation 33 + 43 + 53 = 63 illustrates a relationship in three-dimensional geometry, akin to the Pythagorean theorem in two dimensions. This equation has been recognized for nearly three decades and suggests connections to higher-dimensional objects, potentially involving Euler's work. The discussion emphasizes the relevance of cubic equations in mathematical formulations, particularly those of the form a1k + a2k + ... + amk = b1k + b2k + ... + bnk.

PREREQUISITES
  • Understanding of cubic equations
  • Familiarity with Pythagorean theorem
  • Basic knowledge of higher-dimensional geometry
  • Experience with mathematical programming, specifically FORTRAN
NEXT STEPS
  • Research Euler's contributions to mathematics
  • Explore the implications of cubic equations in geometry
  • Study the applications of 4-D objects in mathematics
  • Learn about mathematical programming techniques in FORTRAN
USEFUL FOR

Mathematicians, educators, students studying geometry, and anyone interested in the relationships between dimensions in mathematical equations.

josdavi
Messages
9
Reaction score
0
I found a special equation about 29 years ago (with a FORTRAN Program) -
3**3 + 4**3 + 5**3 = 6**3

I was/am not a mathematician, not able to fully understand the meaning behind this equation, maybe someone can derive some useful ideas like Pythagoras' theorem.

Is this equation related to 4-D objects ?
 
Mathematics news on Phys.org
i think euler found the same thing (im not sure).
 
That equation has been known for a long time, it' simlair to 3^2 + 4^2 = 5^2 (which is very useful when using pythagoras' theorum) and the like, but in three dimensions.

Obviuosly it is useful in any formula that uses x^3 + y^3 + z^3
 
btw if you are interested in equations of that sort like this one:a1k+ a2k+ ... + amk = b1k+ b2k+ ... + bnk k-exponent n,m-indicators you have this website:http://euler.free.fr/index.htm
 

Similar threads

Undergrad Geometry problem of interest with a 3-4-5 triangle
  • · Replies 59 ·
2
Replies
59
Views
92K
Graduate Are There More Integer Solutions to a^3+b^3+c^3=d^3 Beyond 3^3+4^3+5^3=6^3?
  • · Replies 2 ·
Replies
2
Views
4K
MHB What is the area of a triangle given (2, 3), (4, 5), and (6, 7)?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Negative numbers with fraction problem: simplify 3/4 [ 5/6 ( -18/25 ) + 1/2 ]
  • · Replies 9 ·
Replies
9
Views
3K
MHB Find remainder when (2∗4∗6∗8⋯∗2016)−(1∗3∗5∗7⋯∗2015) is divided by 2017
  • · Replies 2 ·
Replies
2
Views
2K
MHB How does the equation y = 3 + (4/2)x represent Bob's cake baking rate?
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Can One Demonstrate the Ratio Between the Hypotenuses of Two Triangles?
  • · Replies 2 ·
Replies
2
Views
2K
High School Validating Darts Tournament Skill Levels: A Non-Intrusive Approach
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Can We Prove \(a+b^2+c^3+d^4 \le a^2+b^3+c^4+d^5\) Given \(a+b+c+d=4\)?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Can You Prove $6^{33}>3^{33}+4^{33}+5^{33}?
  • · Replies 3 ·
Replies
3
Views
2K