Tag Archives: Aubrey Landry

Mathematics PhD students of Aubrey Edward Landry 

Posted on by

Based on information primarily sourced from the Mathematics Genealogy Project and university records, here are the Ph.D. students in Mathematics who graduated from The Catholic University of America between 1910 and 1950 under the advisement of Professor Aubrey Edward Landry:

1. Sister Mary Gervase Kelley (1917)*
Thesis Title: On the Cardioids Fulfilling Certain Assigned Conditions
2. Joseph Nelson Rice (1917)*
Thesis Title: On the In-and-Circumscribed Triangles of the Plane Rational Quartic Curve
3. Louis Antoine De Cleene (1927)*
Thesis Title: On Triangles Circumscribed about a Conic and Inscribed in a Cubic Curve
4. Frank Engelbert Smith (1928)*
Thesis Title: The Triangles In and-Circumscribed to the Triangular-Symmetric Rational Quartic
5. James Norman Eastham (1931)*
Thesis Title: The Triangles In-and-circumscribed to the Tacnodal Rational Quartic Curve with Residual Crunode
6. Sister Marie Cecilia Mangold (1929)*
Thesis Title: The Loci Described by the Vertices of Singly Infinite Systems of Triangles Circumscribed about a Fixed Conic
7. Sister Leonarda Burke (1931)*
Thesis Title: On a case of the triangles in-and-circumscribed to a rational quartic curve with a line of symmetry
8. Sister Mary de Lellis Gough (1931)
Thesis Title: On the Condition for the Existence of Triangles In-and-Circumscribed to Certain Types of Rational Quartic Curve and Having a Common Side
9. Sister Charles Mary Morrison (1931)*
Thesis Title: The Triangles In-and-Circumscribed to the Biflecnodal Rational Quartic
10. Sister Mary Felice Vaudreuil (1931)*
Thesis Title: Two Correspondences Determined by the Tangents to a Rational Cuspidal Quartic with a Line of Symmetry
11. Sister Mary Domitilla Thuener (1932)*
Thesis Title: On the Number and Reality of the Self-Symmetric Quadrilaterals In-and-Circumscribed to the Triangular-Symmetric Rational Quartic
12. Sister Mary Nicholas Arnoldy (1932)*
Thesis Title: The Reality of the Double Tangents of the Rational Symmetric Quartic Curve
13. Sister Mary Helen Sullivan (1934)*
Thesis Title: The Number and Reality of the Non-Self-Symmetric Quadrilaterals In-and-Circumscribed to the Rational Unicuspidal Quartic with a Line of Symmetry
14. Sister Mary Laetitia Hill (1935)*
Thesis Title: The Number and Reality of Quadrilaterals In-and-Circumscribed to a Rational Unicuspidal Quartic with Real Tangents from the Cusp
15. Sister Mary Henrietta Reilly (1936)*
Thesis Title: Self-Symmetric Quadrilaterals In-and-Circumscribed to the Plane Rational Quartic Curve with a Line of Symmetry
16. Sister Mary Charlotte Fowler (1937)*
Thesis Title: The discriminant of the sextic of double point parameters of the plane rational quartic curve
17. Sister Catherine Francis Galvin (1938)*
Thesis Title: Two Geometrical Representations of the Symmetric Correspondence C(N,N) with Their Interrelations
18. Euphemia Lofton Haynes (1943)*
Thesis Title: Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences
19. Brother Cyprian John McNamara (1948)*
Thesis Title: The Reality of the Double Tangents of the Rational Bicircular Symmetric Quartic

Note, most of these are nuns. Other than Brother McNamara, Landry advised de Cleene (1927) who had received his Holy Orders 8 years earlier.

Landry had three male “civilian” students (Rice, 1917, Smith 1928, Eastham, 1931) and one female “civilian” student (Haynes, 1943). Rice was later hired full time at Catholic University. Eastham was soon hired to teach at Nazareth College. Haynes, 16 years later, was awarded the highest award the Pope (Pope John XXIII) could give to a woman: the Pro Ecclesia et Pontifice medal.

An asterisk next to a name means that I’ve obtain the PhD by inter-library loan (usually from CUA). If there are any additions or missing students, please let me know!

The Beautiful Math of Tangent Lines: Unveiling the Lemniscate’s Secrets

Posted on by

An experimental post

I asked Gemini to create a blog post based on this plot (below) and the Python code I wrote (based on ideas explained to me by Edray Goins) that generated it. (The prompt I fed to Gemini was modified from a prompt found online for generating a blog post about food.) The response, basically unedited, is below. The topic is inspired by the PhD thesis of Euphemia Haynes (a student of Aubrey Landry, Catholic University of America, 1943). See this earlier post for more information on it.

Mathematics can be beautiful, and sometimes that beauty is hidden in plain sight. Take, for instance, this striking image:

a graceful lemniscate curve adorned with a web of tangent lines, all seemingly converging on a single point. This isn’t some artistic rendering; it’s the output of a fascinating algorithm, written in Python and SageMath, plot_lemniscate_quartic_tangents.

This algorithm doesn’t just draw a pretty picture; it solves a sophisticated geometric problem: finding all the tangent lines to a lemniscate quartic that also pass through a specific point on the curve. Let’s dissect the magic:

  1. The Lemniscate: The algorithm begins by defining the lemniscate quartic curve. This curve, shaped like a sideways figure-eight, has a unique and elegant equation: (x² + y²)² = a(x² – y²), where ‘a’ is a constant.
  2. The Target Point: We choose a specific point, P0, on the lemniscate. This is the point where all our tangent lines will magically meet.
  3. The Tangent Hunt: This is where the algorithm gets clever. It doesn’t directly solve for the tangent lines. Instead, it cleverly iterates through numerous points (P) on the lemniscate. For each point, it calculates two things:
    • The slope of the secant line connecting P0 and P.
    • The slope of the tangent line to the lemniscate at point P.
  4. The Convergence: If the slopes from step 3 are approximately equal (within a tolerance), it means the secant line through P0 and P is also a tangent line to the curve at P. This line is added to our collection of tangent lines.
  5. The Reveal: Finally, the algorithm plots the lemniscate along with all the tangent lines it discovered. The result is the captivating image we see—a testament to the hidden geometric relationships within this seemingly simple curve.

The algorithm isn’t just about finding tangents; it reveals a beautiful correspondence between points on the lemniscate and its tangent lines. It’s a visual exploration of the intricate geometry underlying algebraic curves, demonstrating how computation can unveil hidden mathematical beauty. So next time you see a seemingly simple curve, remember the rich and sometimes surprising geometry hiding within.

Remarks on the 1943 PhD  thesis of E. Haynes

Posted on by

Euphemia Haynes was a trailblazer as the first African-American woman to earn a doctorate in mathematics. The Catholic University of America holds a copy of her thesis, entitled “The Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences”, in their archives. 

A short biography: Euphemia Lofton daughter of Dr William Lofton, a dentist, and Lavinia Day Lofton, a kindergarten teacher. She was the valedictorian of M Street High School in 1907 and then graduated from (what is now known as) University of the District of Columbia with distinction and a degree in education in 1909. She was a  mathematics major at Smith College, which she graduated from in 1914. She married Harold Appo Haynes, a teacher in 1917 and earned her master’s degree in education from the University of Chicago in 1930. In 1943 she was awarded her PhD from The Catholic University of America, advised by Professor Aubrey E. Landry. An excellent, more detailed biography can be found at [KSZ] (see also http://www.math.buffalo.edu/mad/PEEPS/haynes.euphemia.lofton.html).

More of her biography is given in the post The Mathematician and the Pope, also available on this blog.

In this blog post, we merely try to explain her title. What is a “symmetric correspondence”?

We refer to Dolgachev’s notes [Do14], section 5.5: A correspondence of degree d between nonsingular curves X and Y is a non-constant morphism T:X\to Y^{(d)} to the d-th symmetric product Y^{(d)} of $Y$. Its graph is denoted \Gamma_T\subset X\times Y. The projection \Gamma_T\to X is a finite map of degree $d$, while the projection \Gamma_T\to Y is a finite map of degree e, say. It defines a correspondence Y\to X^{(e)} denoted by T^{-1}, called the inverse correspondence. Its graph \Gamma_{T^{-1}}\subset Y\times X is the image of \Gamma_T under the swap X\times Y\to Y\times X. If d is the degree of T and e is the degree of T^{-1}, we say that $T$ is a correspondence of type (d, e). This correspondence is symmetric if T = T^{-1}. 

Very roughly speaking, in her thesis, Haynes looks at various special cases of curves and in these cases she derives (technically defined) conditions that characterize the types of symmetric correspondences that arise in those cases.

While a scan of her thesis is archived at Catholic University, I have typed up her thesis in latex. For a digital copy, just email me (wdjoyner@gmail.com).

References

[Do14] I. Dolgachev, Classical Algebraic Geometry: a modern view, Cambridge Univ. Press, 2012.

(at https://mathweb.ucsd.edu/~eizadi/207A-14/CAG.pdf)

[KSZ17] Susan Kelly, Carly Shinners, Katherine Zoroufy, “Euphemia Lofton Haynes: Bringing Education Closer to the “Goal of Perfection“, preprint, 2017 (available at https://arxiv.org/abs/1703.00944). A version of this paper was also published in the Notices of the American Mathematics Society.