Solving the Quartic with a Pencil
نویسنده
چکیده
One might say that this formula allows one to solve the quadratic with a pencil. There is an analogous formula for the general quartic equation, ax+ bx + cx + dx+ e = 0. If you just have to know the formula or one way to derive it and don’t care about anything else, you may just skip to the last section of this paper. However, there is a mathematical notion of a pencil, which is rather cool and has gained prominence in geometry in recent years. In what follows pencils will be described and then used to solve the general quartic.
منابع مشابه
Halphen Pencils on Quartic Threefolds
∼= P, where g(x, y, z) = 0 is a homogeneous equation of the curve Z and (λ, μ) ∈ P. Then a general curve in P is birational to an elliptic curve. Remark 1.1. The construction of pencil P can be generalized to the case when C has at most ordinary double points and the points P1, · · · , P9 are not necessarily distinct (see [3]). The pencil P is called a standard Halphen pencil. Definition 1.2. A...
متن کاملIntuitionistic fuzzy stability of a quadratic and quartic functional equation
In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.
متن کاملA Rare Penetrating Trauma of Both Orbit and Nasal Cavity
Introduction: Diagnosis of orbital foreign body (FB) penetration is usually obvious when part of the FB is still attached at the entry wound (1). However, the depth and course of the FB in this case was not visible. Case Report: A 5-year old female presented with a pencil penetrating the left orbit. A computed tomography (CT) scan showed that the pencil penetrated the left orbit (extraseptal)...
متن کاملA QUARTIC POTENTIAL FOR THE NUCLEONIC QUARKS
We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...
متن کاملConstruction of a surface pencil with a common special surface curve
In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $vec{W}_{0} $ of a surface curve $vec{r}(s)$ and unit surface normal $vec{n} $ along the curve $vec{r}(s)$ satisfy the condition $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. We point out that a $D$-type curve is a geodesic curve or an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 114 شماره
صفحات -
تاریخ انتشار 2007