Puzzling Visual Maths For The Curious Minded #1  
     
  archimedes lab logo
Archimedes Laboratory Project

Mental & Perceptual Activities that Enhance Critical and Creative Thinking Skills

Social Media Contact us Like us on Facebook Circle us on Google+ Follow us on Twitter Pin it Thumb up this page

 

 

Puzzling Visual Maths

Loading...

Button Backward

Hydrostatic Solution Of Particular Trinominial Equations Button Forward
 

A. Demanet devised an interesting method of solution of trinomial equations which depends on the use of communicating vessels of convenient forms.
To solve an equation of the third degree of the form:
x3 + x = c
where c is a constant, an inverted cone and a cylinder, joined together by means of a tube, are taken.
As shown below.

Hydrostatic Solution of Trinominial Equations

 

The radius r of the cone and its height h are in the ratio:
r/h = √3/√π
while the base of the cylinder is taken as 1 cm2

If c cubic centimeters of water are poured into one of the two vessels, the water will rise to the same height h in both. The volume of water contained in the cone will be h3, that in the cylinder h, so that we get:
h3 + h = c
Therefore, by measuring the height h of the water we obtain a solution of the equation.

In the case of the equation
x3 - x = c
the cone alone is used, and a solid cylindrical piece whose base is 1 cm2 is introduced. The volume c of water poured in will thus be the difference between h3 and h, and therefore h, the height of the liquid, is again a solution.

By a substitution z = xp we can reduce all reducible equations of the third degree such as:
x3 + pz = q
where p and q are given positive numbers, to the form x3 + x = c

 

 
 

*Source: page 253 of “Matematica dilettevole e curiosa” by I. Ghersi

You can comment and discuss this puzzle on our FaceBook fan page.

 

From the same Author
Impossible Folding Puzzles
Impossible Folding Puzzles
Pliages, dĂcoupages et magie
Pliages, découpages & magie

Math products
Postcards
Postcards
T-shirt man
T-shirt man
T-shirt girl
T-shirt girl
 
     
 
 

archimedes lab logoArchimedes Laboratory Project
Mental & Perceptual Activities that Enhance
Critical and Creative Thinking Skills

Social Media Contact us Like us on Facebook Circle us on Google+ Follow us on Twitter Pin it Thumb up this page
arrow 1ABOUT arrow 1SITEMAP arrow 2 SERVICES arrow 2 PRODUCTS arrow 1SUBMIT arrow 1ADVERTISE arrow 1CONTACT
 

 

   For Publishers
   Workshops
  Books
  Puzzles
  Prints & Posters
  Illusory Art
     
Archimedes in the bathtub
 
Contact us Like us on Facebook Circle us on Google+ Follow us on Twitter Pin it Thumb up this page
 
  © 1997-2014 G. Sarcone [Archimedes-lab.org] All rights reserved  
  Creative Commons LicenseArchimedes Laboratory™ by Gianni A. Sarcone is licensed under a
Creative Commons Attribution - NonCommercial - NoDerivatives 4.0 International License