Ancient observers used rocks to track the sun, marking the solstices and equinoxes and comparing spring–summer to fall–winter lengths, while previewing Excel or Google Sheets calculations.

Predict the moon’s position at any time by using a 24-hour clock, mapping sun-moon relationships and phases from first quarter to full, with hands-on practice.

Learn how the zodiac maps the sun's yearlong path through constellations, how planets and the moon align with the ecliptic, and what causes eclipses, based on ancient observations.

Use a sun clock to visualize the sun’s daily path and moon’s phases with sun and moon hands; sunrise is in the east, sunset in the west, reversed for teaching.

Explore how four observations lead to a barrel-shaped earth: ships disappear from the bottom, star positions change with north-south travel, yet stay fixed east-west.

Define diameter and radius, and relate them to the circumference. Explore pi and 3.14, 360-degree circles, and the historical origins from Babylonians to William Jones.

Learn how parallel lines reveal equal corresponding angles to calculate the earth's size, building on a circles-based method from the previous experiment.

Learn cross-multiplication to solve proportions by setting two equal fractions, starting with the x, multiplying diagonally, then dividing to find the missing value.

Explore triangles: three sides A, B, C and three angles x, y, z, summing to 180 degrees. Learn about opposite, adjacent, and the hypotenuse, with theta as the unknown angle.

Explore how triangles relate sides and angles, using sine theta and sine tables to estimate angles and lengths in right triangles.

Explore how the sun’s larger size creates the Earth's shadow as a triangle that shrinks with distance, and apply simple math to estimate the moon’s size through lunar eclipse measurements.

Observe a lunar eclipse to measure Earth’s shadow with a moon-sized reference, concluding the shadow is 2.75 moon diameters wide and inferring Earth and moon sizes.

Learn to compute a triangle’s width at a given height using the width-to-height ratio from base and height, and see this method apply to the moon in the next video.

Compute the moon’s diameter from a lunar eclipse by mapping sun–earth–moon geometry, showing the moon is about 0.28 Earth diameters, roughly 2160 miles wide.

Calculate a triangle's width at any height by dividing width by height, then apply the same method to a line to estimate the moon's size in the next video.

Apply the 1 to 25 thumb width rule to estimate the moon's distance, then deduce the sun's distance and the Earth's orbital length.

Explore how the sun's daily motion and shadows reveal Earth's roundness, measure Earth and Moon sizes and distances, and explain why ancient skeptics doubted planetary motion.

Track how knowledge grows within bubbles of ideas, from ancient Greece through Copernicus to Newton, as Plato and Aristotle clash over observation, circles, and the sun-centered model.