The algebrista
If you like geeky TV shows, I particularly recommend Bones s06ep08 entitled “The Twisted Bones in the Melted Truck”. The title alone should convince the best of you who know that it is impossible to twist bones because bones don’t melt ! But these guys are the specialists, so they will really find twisted bones and even provide a scientific explanation to that [1]. What’s even stronger is that they untwist them just for your pleasure. Check this out !
ALL THE RIGHTS OF THE CLIPS BELONG TO THE CHANNEL FOX. This video is used for comment purpose of Bones season 6 episode 8 where it is stated that Gerolamo Cardano wrote a set of mathematical equations to describe the skeleton system. Believing that comment and critique are at the very core of the fair use doctrine as a safeguard for freedom of expression, we claim it is a fair use under copyright law.
I should confess that I wasn’t familiar with Gerolamo Cardano prior to this. Cardano is a famous algebraist known for his publication of the solutions to the cubic and quartic equations. And as there is no general algebraic solution to polynomial equations of degree five or higher [2], Cardano couldn’t do more. Besides he was the first to publish the use of complex numbers in calculations even if he did not understand their properties. Among his many other contributions, he invented the Cardan shaft with universal joints and published the horoscope of Jesus… Concerning the set of mathematical equations written by Cardano to describe the skeleton system mentioned in this episode of Bones, I found no reference of their existence.
If Cardano didn’t publish such equations, why did the scriptwriters made reference to him there ? They have obviously done some research, but maybe it’s a confusion due to the fact that in Biomechanics, angles named “cardan angles” can be used to describe the kinematic of the limbs [3]. Another plausible explanation can be found looking for the etymology of the word “algebra”. It comes from Arabic al-jebr and refers to the setting or the straightening out of broken bones, to the “reduction” of a fracture. In Spanish “algebrista” still designs a bonesetter. In Mathematics, the word has been introduced in 820 by al-Khwārizmī to describe the operations of “reduction” and balancing, i.e. the cancellation of like terms on opposite sides of the equation [4]. Nowadays one still talks of “reducing” fractions to lowest terms. Knowing this, Cardano’s 1545 book title Artis Magnæ, Sive de Regulis Algebraicis could be translated by About The Great Art, or The Rules of Bone Setting… (Mmmmh…) A bit too subtle maybe?
Notes
- See K. Killgrove comments about that.
- Abel’s impossibility theorem
- S. J. Tupling and M. R. Pierrynowski, “Use of cardan angles to locate rigid bodies in three-dimensional space”, Medical and Biological Engineering and Computing, Vol. 25, Nb. 5, pp. 527-532, 1987.
- C. B. Boyer and U. C. Merzbach, “A History of Mathematics”, second edition, John Wiley & Sons, 1991, ISBN0471543977.
ths1104 
,
in these cases are used many situations observed prof dr mircea orasanu and prof drd horia orasanu that appear in CONSTRAINTS OPTIMIZATION and accepted by prof dr Constantin Udriste
in many situations and excepted appear important aspects that evidence main and high properties observed prof dr mircea orasanu and prof drd horia orasanu for remainder theorem and followed as say and prof dr Constantin Udriste concerning CONSTRAINTS OPTIMIZATION for non holonomy problem as fundamental element so called LAGRANGIAN OPERATOR ,and then that motion of an particle moving in one dimension under the action of a conservative force is, in principle, integrable. Since $K=(1/2)\,m\,v^2$, the energy conservation equation (46) can be rearranged to give
\begin{displaymath} v = \pm\left(\frac{2\,[E-U(x)]}{m}\right)^{1/2}, \end{displaymath} (52)
where the $\pm$ signs correspond to motion to the left and to the right, respectively. However, since $v=dx/dt$, this expression can be integrated to give
\begin{displaymath} t=\pm\left(\frac{m}{2\,E}\right)^{1/2} \int_{x_0}^x\frac{dx’}{\sqrt{1-U(x’)/E}}, \end{displaymath} (53)
where $x(t=0)=x_0$. For sufficiently simple potential functions, $U(x)$, the above equation can be solved to give $x$ as a function of $t$. For instance, if $U=(1/2)\,k\,x^2$, $x_0=0$, and the plus sign is chosen, then
\begin{displaymath} t = \left(\frac{m}{k}\right)^{1/2}\int_0^{(k/2\,E)^{1/2}\,x}… …/2} \sin^{-1}\left(\left[\frac{k}{2\,E}\right]^{1/2} x\right), \end{displaymath} (54)The above discussion suggests that the motion of an particle moving in a potential generally becomes less bounded as the total energy $E$ of the system increases. Conversely, we would expect the motion to become more bounded as $E$ decreases. In fact, if the energy becomes sufficiently small then it appears likely that the system will settle down in some equilibrium state in which the particle is stationary. Let us try to identify any prospective equilibrium states
as is used must to find that prof drd horia orasanu search more time solutions and followed these utilizing important considerations specially for CONSTRAINTS OPTIMIZATIONS that represent a view points in optimizations problem and other considered by prof dr Constantin Udriste and the most important outstanding problem has been to formulate equation in a rigorous way by making the Hamiltonian constraint into a well-defined operator. Just before the workshop began, The idea was to quantize these, making them into operators acting on wavefunctions on the space of 3-metrics, and then to quantize the Hamiltonian and diffeomorphism constraints and seek wavefunctions annihilated by these quantized constraints To do the above integration 4 line integrals, one for each side of the square, must be evaluated. (In this case C = C_1+C_2+C_3+C_4.) This is a good case for using Green’s theorem
in many situations observed as prof dr mircea orasanu and prof drd horia orasanu followed as solved of equations We now need to show that the countable union of measurable sets is measurable.
First note that if we can assume that the are disjoint. Here is why: Let , , and so on. Then and the are mutually disjoint. So we can assume with no loss of generality that the have this property.
Note: I am getting tired of the “tilde” notation and so will be using the notation to denote the set complement.
Now let . Then is measurable and . Then:
By finite additivity Hence we can substitute into the right hand side of the inequality to obtain:
This is true for all values of
This means ; the latter inequality following from countable subaddivity.
4. Now we can show finite additivity for for disjoint measurable sets in Lebesgue measure (no lo
If you like geeky TV shows, I particularly recommend Bones s06ep08 entitled “The Twisted Bones in the Melted Truck”. The title alone should convince the best of you who know that it is impossible to twist bones because bones don’t melt ! But these guys are the specialists, so they will really find twisted bones and even provide a scientific explanation to that [1]. What’s even stronger is that they untwist them just for your pleasure as say prof dr mircea orasanu in a discussion with cardano and Adrien LEGENDRE
.
as in many times appear important aspects of CARDANO Equation observed prof dr mircea orasanu and prof drd horia orasanu when are possible important developments and other aspects Phase transition and heat engine efficiency of phantom AdS black holes are investigated with peculiar properties found. In the non-extended phase space, we probe the possibility of $T-S$ criticality in both the canonical ensemble and grand-canonical ensemble. It is shown that no $T-S$ criticality exists for the phantom AdS black hole in the canonical ensemble, which is different from the RN-AdS black hole. Contrary to the canonical ensemble, no critical point can be found for neither phantom AdS black holes nor RN-AdS black hole in the grand-canonical ensemble. Moreover, we study the specific heat at constant electric potential. When the electric potential satisfies $A_0>1$, only phantom AdS black holes undergo phase transition in the grand-canonical ensemble. In the extended phase space, we show that there is no $P-V$ criticality for phantom AdS black holes, contrary to the case of the RN-AdS black hole. Furthermore, we define a new kind of heat engine via phantom AdS black holes. Comparing to RN-AdS black holes, phantom AdS black holes have a lower heat engine efficiency. However, the ratio $\eta/\eta_C$ of phantom AdS black hole is higher, thus increasing the possibility of approaching the Carnot limit. This observation is obviously of interest. The interesting results obtained in this paper may be attributed to the existence of phantom field whose energy density is negative.
thus that CARDANO equations are used in many applications observed prof dr mircea orasanu and prof drd horia orasanu as followed GERGONNE Problem ,PONCELET Theory La VERRIER developments or CONSTRAINTS OPTIMIZATIONS and mire
,
, ,
must considered the Ruffini method for algebraic equation with grad five observed prof dr mircea orasanu and prof drd horia orasanu for solved and cardano equations and also important problem of GALOIS AND LEGENDRE that has influenced by GALOIS EVARISTE how is said
modern algebra: Group theory
…was by the French mathematician Évariste Galois (1811–32) to settle an old problem concerning algebraic equations. The question was to decide whether a given equation could be solved using radicals (meaning square roots, cube roots, and so on, together with the usual
Galois’s manuscripts, with annotations by Joseph Liouville, were published in 1846 in the Journal de Mathématiques Pures et Appliquées\But it was not until 1870, with the publication of Camille Jordan’s Traité des Substitutions, that group theory became a fully established part of mathematics.
after Cardan’s Ars Magna many mathematicians(x – b)(x – c)(x – d) = 0. Leibniz wrote a letter to Huygens in March 1673. In it he made many contributions to the understanding of cubic equations. Perhaps the most striking is a direct verification of the Cardan-Tartaglia formula. This Leibniz did by reconstructing the cubic from its three roots (as given by the formula) as Harriot claimed in general. Nobody before Leibniz seems to have thought of this direct method of verification. It was the first true algebraic proof of the formula, all previous proofs being geometrical in nature.
and thus here prof dr mircea orasanu and prof drd horia orasanu have a more contributions for F Viette and Ruffini equations as (-q)2 -4(p + 2y)(p2 – r + 2py + y2) = 0.Rewrite this last equation as
(q2 – 4p3 + 4 pr) + (-16p2 + 8r)y – 20 py2 – 8y3 = 0
to see that it is a cubic in y.
,