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The quadrifolium is the 4-petalled rose curve having n=2. It has polar equation r=asin(2theta) (1) and Cartesian equation (x^2+y^2)^3=4a^2x^2y^2. (2) The area of the ...

The quartic formula is a name sometimes given to one of the related explicit formulas for the four roots z_1, ..., z_4 of an arbitrary quartic equation with real coefficients ...

A quasi-regular graph is a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 (Bozóki et al. 2020). ...

A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not ...

A quintic symmetric graph is a quintic graph (i.e., regular of degree 5) that is also symmetric. Since quintic graphs exist only on an even number of nodes, so do symmetric ...

R(p,tau)=int_(-infty)^inftyint_(-infty)^inftyf(x,y)delta[y-(tau+px)]dydx, (1) where f(x,y)={1 for x,y in [-a,a]; 0 otherwise (2) and ...

Given a straight segment of track of length l, add a small segment Deltal so that the track bows into a circular arc. Find the maximum displacement d of the bowed track. The ...

Let ad=bc, then (1) This can also be expressed by defining (2) (3) Then F_(2m)(a,b,c,d)=a^(2m)f_(2m)(x,y), (4) and identity (1) can then be written ...

Oloa (2010, pers. comm., Jan. 20, 2010) has considered the following integrals containing nested radicals of 1/2 plus terms in theta^2 and ln^2costheta: R_n^- = (1) R_n^+ = ...

Following Ramanujan (1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...