Award-Winning Projective Geometry
Tutors
Award-Winning
Projective Geometry
Tutors
Private 1-on-1 tutoring, weekly live classes for academic support, test prep & enrichment, practice tests and diagnostics, and more to elevate grades and test scores.
Based on 3.4M Learner Ratings
UniversitiesSchools & Universities
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ProficiencyGrowth in Proficiency
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I am an interdisciplinary educator with an Ed.M. from the Harvard Graduate School of Education and a B.A. from Dartmouth College. My background is primarily in integrated arts learning and museum education and I specialize in visual arts, history and art history, and object-based learning. In all subjects, I take a creative, inquiry-based and learner-centered approach, designing opportunities for each unique individual to meet their learning goals.

I'm not tutoring or buried in my textbooks, you will either find me rock climbing at the Triangle Rock Club, playing Ultimate Frisbee, working on my car, or enjoying the great outdoors (beaches, mountains, forests--you name it, I love it). On rainy weekends I enjoy tinkering with computers and old electronics, playing Pokemon, or picking at my guitar.
I am a recent graduate from a masters program in biostatistics at Columbia University. I received my Bachelor of Arts in biological sciences, with a focus in neurobiology at Northwestern University. In August, I will be starting a doctoral program in biostatistics at NYU. I was a teaching assistant at Columbia University in my department and also have tutored graduate students and undergraduates privately as well. My primary areas of tutoring are math and statistics coursework in addition to math sections on standardized tests such as the GRE and GMAT. I am very passionate about helping students feel more confident and excited about math. In my spare time, I enjoy running, playing piano, and spending time with friends and family.
I am a graduate of Wesleyan University, where I received my Bachelor of Arts in Sociology with High Honors. With eight years of experience working in education, I've tutored students in math, science, history, and English, as well as helped students prepare for standardized tests. I've guided adults towards passing the US Citizenship Exam and taught English in India, where I lived for six months. Whenever I work with a student I personalize the lessons to fit their particular learning style, since I know every student is unique and having the right fit can make all the difference in making learning fun and effective. My strengths are tutoring the social sciences and humanities, as well as making math and standardized tests approachable to students that normally don't like those subjects. In my spare time I like traveling, spending time in the outdoors (climbing & backpacking), meditation, and playing soccer. Next fall I will be beginning my PhD in Education at Harvard University.
I'm Solange - a recent graduate from Harvard where I studied Sociology & Women's Studies. I've been tutoring for eight years now, and have worked with a wide range of ages and in a wide range of subjects. Some of my specialties are college prep/test taking II worked in the admissions office on campus); social sciences; and literature/writing.
I am a junior Mechanical Engineering major at Yale, and I hope to become a Naval Aviator after college. I am also a varsity sailor, and enjoy playing music with friends when I can get some free time. I have been tutoring my fellow students throughout my entire academic career, and I would best describe my tutoring style as one that adapts to each students' needs. For example, I have always tried to frame questions in a different way so that the student can better understand the question. Some students need visual representations of numbers and systems to understand them, and others benefit more by understanding the concepts behind each formula. I prefer to tutor in math and physics, and especially with real world application problems. I hope to help students improve their standardized test scores and their understanding of the math and sciences so that they can achieve their academic goals!
I am a graduate of Washington University in St Louis, where I received my Bachelor of Arts in History with minors in Humanities and Anthropology. Since graduation, I have worked as a tutor, teacher, and director of tutors at a charter public middle school in Boston. During this time I also received my Masters in Mild to Moderate Disabilities from Simmons College. I have worked extensively with students with a range of abilities, including students with specific learning disabilities, emotional impairments, dyslexia, and ADHD. My teaching experience has given me a deep understanding of the knowledge and habits essential to academic success and has given me the opportunity to hone a variety of strategies that ensure students at each level can achieve their academic goals. While I tutor a broad range of subjects, my favorite ones are Reading, Elementary/Middle School Math, History, and Test Prep. In my experience, tutoring is the most rewarding when a student has that "aha!" moment and achieves a new level of understanding and confidence in his/her abilities. I am a firm believer in the transformative power of education, and I see my role to be that of a facilitator and coach who is there to help the student reach his/her goals through individualized support and rigorous practice. In my free time, I enjoy reading, running, practicing my Spanish, and discovering new music. I am also an avid traveler and just got back from a 3 month trip to South America. I look forward to the opportunity to work with you!
I am a rising sophomore at Harvard College and am about to declare as a Mechanical Engineering concentrator, working towards a Bachelor of Science degree. I've always enjoyed sharing my knowledge with my peers and those around me and have done so in both formal and informal settings. I've been a tutor for both Math and Spanish programs in high school and enjoyed the strides I made with students. I am willing to tutor any subject I have a background in, but am strong in mathematics, the sciences, Spanish, history, writing, and ACT prep. I enjoy teaching mathematics most due to the joy I can see in children once they master a topic and can answer even pointed questions meant to stump them, and maybe even put their knowledge to real world use. As a tutor, I like to give a strong foundation to orient my student, and then gradually grant them more freedom and independence until they can feel themselves grasp the concept, pointing out pitfalls or common errors along the way; teachers who used these methods on me always left the most lasting impressions. Outside of my studies, I really enjoy listening to music, both old favorites and new interests, reading classics, and gaming/playing basketball with my friends.
I am proud to be a part of Varsity Tutors! I am originally from San Antonio, TX; I completed my undergraduate education at Rice University in Houston where I received a bachelor's degree in Biochemistry and Cell Biology. Currently, I am in my second year of medical school at Baylor College of Medicine.
I am an aspiring applied mathematician, with particular interest in image processing and climate science. I graduated in May 2017 from Washington University in St. Louis with a bachelor's in physics and mathematics, and am beginning a PhD program in September 2017 at the University of Chicago in Computational and Applied Mathematics. I've tutored introductory physics students for three years and enjoyed it thoroughly, as a chance to help other students while revisiting fundamental concepts to enhance my own knowledge. I'm eager to continue reaching out and helping students of math and physics to succeed and, furthermore, to appreciate the beauty and power of these subjects.
I am a graduate of the University of Chicago where I received my undergraduate degree in political science. Right after graduation, I worked as an academic and test prep tutor as well as admissions consultant in Hong Kong. For the past two years, I worked with a number of students to help prepare them for college in the United States.
I am comfortable tutoring math subjects up to multivariable calculus and differential equations, as well as college physics.
Testimonials
Because the right Projective Geometry tutor makes all the difference.
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Frequently Asked Questions
Projective geometry studies properties of geometric figures that remain unchanged under projection—essentially what you see when you look at objects from different angles or distances. Unlike Euclidean geometry, which focuses on measurements like distance and angles, projective geometry emphasizes how points, lines, and shapes relate to each other structurally. A key difference is that in projective geometry, parallel lines meet at a "point at infinity," which opens up entirely new ways of thinking about space and perspective. Understanding this conceptual shift from metric properties to projective properties is crucial for appreciating why projective geometry matters in art, architecture, computer graphics, and advanced mathematics.
Projective geometry proofs require a different mindset than Euclidean proofs because they rely on abstract structural relationships rather than concrete measurements. Many students initially try to use familiar tools like the Pythagorean theorem or angle measures, which don't apply in projective settings. The real challenge is learning to think visually and structurally—recognizing collinearity, cross-ratios, and duality without falling back on metric reasoning. A skilled tutor helps students build confidence by breaking complex proofs into logical steps, showing how to identify which projective properties apply to each situation, and helping them see the elegant patterns that make these proofs work.
Cross-ratios and harmonic division are foundational concepts in projective geometry, but they feel abstract at first because they don't connect to everyday intuition the way distance does. The key is to work with concrete examples—start with specific points on a line, calculate the cross-ratio step by step, and notice how it stays the same under projection. Understanding that cross-ratios measure how four points relate to each other structurally helps you see why this property is so powerful across different geometric contexts. Personalized tutoring makes this click by having you work through multiple examples with increasing complexity, recognizing patterns, and building confidence in applying cross-ratios to prove more sophisticated results.
Duality is one of the most elegant aspects of projective geometry—it's the principle that points and lines play symmetric roles, so many theorems about points automatically have dual versions about lines. This isn't just a clever mathematical trick; it reveals deep structure in geometry and helps you understand why certain relationships exist. For example, Desargues' Theorem and its converse both illustrate duality in action. Learning to recognize and use duality helps you prove theorems more efficiently and deepen your conceptual understanding of how projective geometry works. A tutor can help you see duality as a powerful problem-solving tool rather than an abstract concept.
Projective geometry is the mathematical foundation for perspective in art and the geometry behind how computers render 3D scenes on 2D screens. When Renaissance artists developed perspective techniques, they were intuitively using projective principles—parallel lines receding toward a vanishing point, for instance. In computer graphics, understanding how projections work is essential for ray tracing, camera transformations, and rendering. Seeing these real-world connections helps make abstract projective concepts feel tangible and relevant. A tutor can use concrete examples from photography, architecture, and digital design to show why the theory matters and help you appreciate the beautiful interplay between pure mathematics and practical applications.
Projective conics (ellipses, parabolas, and hyperbolas viewed through a projective lens) are unified in a way that Euclidean geometry doesn't show—projectively, they're all the same type of curve, distinguished only by how they interact with the line at infinity. To build strong understanding, focus on how conics behave under projection, what properties remain invariant, and how to work with them algebraically in homogeneous coordinates. The shift from thinking about conics as separate types to recognizing their underlying unity is a major conceptual milestone. Personalized instruction helps you recognize that this unified view isn't just elegant—it simplifies many proofs and opens doors to deeper results in algebraic geometry.
Many students initially approach projective geometry by memorizing formulas and procedures, but true mastery comes from understanding the underlying concepts and seeing how different ideas connect. A skilled tutor helps you recognize structural patterns, asks questions that prompt you to think more deeply about why theorems work rather than just how to apply them, and guides you toward making your own discoveries. This shift—from "how do I solve this?" to "why does this structure work this way?"—builds genuine confidence and makes advanced topics feel less intimidating. Personalized tutoring is particularly valuable here because a tutor can identify where your conceptual gaps are, adjust explanations to match your thinking style, and celebrate the moments when abstract ideas suddenly click.
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