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Proposition I.4 presents Euclid’s proof of what is called the “Side-Angle-Side Theorem” in modern schools. The question students often ask is in Classical Geometry, when studying proposition 1.4 is, “How can we just assume the two triangles with two equal sides and a common angle between them?” That does seem to come out of nowhere. These two imagined triangles can be produced using the Elements and Propositions I.1-3. See image above. To summarize: Those who have studied propositions I.1-3 should be able to see how this was done. Follow the letters in alphabetical order. I haven’t formally proven this yet, … Continue

The minute one enrolls in college, the costs begin. Tuition is due as the first classes begin and students don’t pay for a college degree, they pay to attend college. Many students are scammed into terrible situations by colleges that serve little purpose other than to fund their own operation. A number of statistics give parents an insight into what’s really going on at different colleges–and these stats aren’t mentioned much. Admission Rate Colleges receive applications and, supposedly, select the best candidates. The quality of student admitted to a college is very important because these students are our children’s roomates, … Continue

Great video for students in classical mathematics in the Classical Liberal Arts Academy. Confirms the truth that the Greeks learned from the ancient Babylonians, as the ancients said they did. “Past civilizations understood mathematics a lot better than we thought.” We argue that past civilizations understood EVERYTHING a lot better than modern scholars thought–and continue to think.

When I was 17 years old, the thought of what happens at the moment of death awakened in me an interest in religion. As an unbeliever, I asked, “When I die, do I just stop existing?” The question haunted me and led me to seek the doctrine of the resurrection in Christianity, which Reason shows us must be true. In the Summa Contra Gentiles, St. Thomas Aquinas provides the proof that the human soul does not perish when the body is corrupted. 1. It can be clearly shown that the human soul is not corrupted when the body is corrupted. … Continue

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The problem with modern education is organizational and practical. It made sense in the 1900s, when it was invented. It does not make any sense in 2024. Consider the image below, which represents the modern school model: We see that students of varying abilities (represented by colors) are collected into large groups by age. Their education is provided by a large staff of specialists, also of varying abilities and stability (also represented by colors). It’s worth noting that staff turnover in schools is close to 30%, so the teachers in grey will need to be replaced next year. Over this … Continue

In modern schools, a teacher provides a “syllabus” to students because, without a syllabus, no one has any idea what will be taught in the course.  Not only do parents and students not know what will be taught in a modern school course, but most school administrators don’t know either.) Though books may be required for courses, teachers may pick and choose what they will cover in the course, and require whatever they please on their quizzes and tests.  The teacher controls the content of the course and that content can change from one teacher or school to another, and … Continue