Science Milestones: A New Astronomy with Johannes Kepler

Each month, I like to share a post celebrating the accomplishments of a scientist whose discoveries and advancements have made a significant difference in our lives. To honor the work of these amazing people, I provide a little peak into their life and share an unschool-style learning guides or unit study to guide you and your children on a path of discovery.

This month, I chose to honor the Johannes Kepler, who lived in an era when there was no clear distinction between astronomy and astrology. There was, however, a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy).

Science Milestones: A New Astronomy with Johannes Kepler @EvaVarga.netJohannes Kepler

In 1596, the German astronomer published his first important work on astronomy, Mysterium Cosmographicum (The Cosmographic Mystery). As well as defending the heliocentric model of the universe previously proposed by Copernicus in 1543.

Kepler explained the orbits of the known planets around the Sun in geometric terms in an attempt to unravel “God’s mysterious plan of the universe.” To do this, he dow upon the classical notion of the “harmony of the spheres” which he linked to the five Platonic solids – octahedron, icosahedron, dodecahedron, tetrahedron, and cube.

Science Milestones: A New Astronomy with Johannes Kepler @EvaVarga.net

The Platonic solids, when inscribed in spheres and nested inside one another in order, correspond to the orbits of the planets Mercury, Venus, Earth, Mars, Jupiter, and Saturn.

In 1619, he published Harmonices Mundi (The Harmony of the World) wherein he stated his third law of planetary motion. He described the relationship between a planet’s distance from the Sun and the time taken to orbit around it as well as the speed of the planet at any time in that orbit.

Biography

Science Milestones: Johannes KeplerKepler was born in the small town of Weil der Stadt in the Swabia region of Germany and moved to nearby Leonberg with his parents in 1576. His father was a mercenary soldier and his mother, the daughter of an innkeeper. Johannes was their first child.

When Johannes was just five, his father left home for the last time and is believed to have died in the war in the Netherlands. As a child, Kepler lived with his mother in his grandfather’s inn. He tells us that he used to help by serving in the inn.

Kepler’s early education was in a local school and then at a nearby seminary. Intending to be ordained he went on to enroll at the University of Tübingen, a bastion of Lutheran orthodoxy.

Throughout his life, Kepler was a profoundly religious man. All his writings contain numerous references to God, and he saw his work as a fulfilment of his Christian duty to understand the works of God.

At Tübingen Kepler was taught astronomy by one of the leading astronomers of the day, Michael Mästlin. The curriculum was of course, geocentric astronomy, in which all seven planets – Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn – moved around the Earth, their positions against the fixed stars being calculated by combining circular motions.

This system was more or less in accord with current Aristotelian notions of physics, though there were certain difficulties. However, it seems that on the whole astronomers were content to carry on calculating positions of planets and leave it to natural philosophers to worry about whether the mathematical models corresponded to physical mechanisms. Kepler did not take this attitude. His earliest published work, Mysterium Cosmographicum, proposed to consider the actual paths of the planets, not the circles used to construct them.

 “I am satisfied…to guard the gates of the temple in which Copernicus makes sacrifices at the high altar.” ~ Johannes Kepler

Kepler was one of the few pupils to whom Mästlin chose to teach more advanced astronomy by introducing them to the new, heliocentric cosmological system of Copernicus. Kepler seems to have accepted almost instantly that the Copernican system was physically true.

Soon after moving to Regensburg in 1630, he became seriously ill with fever and on November 15 he died.

Bring it Home

What are Kepler’s three laws of planetary motion? How were his ideas viewed by his contemporaries?

Learn more about star polyhedra, discovered by Kepler in 1619 and prominently featured in the architecture of European churches.

Build models of the five Platonic solids; consider The Finnish Craft of Himmeli or Paper Models of Polyhedra.

Research the epitaph inscribed on his gravestone (sadly swept away in the Thirty Years War):

I used to measure the heavens,
now I shall measure the shadows of the earth.
Although my soul was from heaven,
the shadow of my body lies here.

 

Science Milestones

Visit my Science Milestones page to learn more about scientists whose discoveries and advancements have made a significant difference in our lives or who have advanced our understanding of the world around us.

Interested in learning about others who were born in the month of January? Hop over to Birthday Lessons in December to read posts by other iHomeschool Network bloggers.

Life of Fred: Math Curricula for Middle & High School

As a homeschool parent, I want to challenge my children. I want to provide them with opportunities not available to students in brick-and-mortar schools. I spent a lot of time researching and seeking out course work and math curricula that was engaging and challenging.

Years ago, a homeschool colleague shared with me that her 14 year old daughter had taken the college placement exam and had enrolled in Math 111. I immediately wanted to know what math curricula she had used. “Life of Fred,” she replied. “Chloe worked through the Pre-Algebra series and Beginning Algebra on her own.” 

math curricula review

Disclosure: This post contains affiliate links which generate commissions when you purchase through that link.

Each Life of Fred text is written in the style of a novel with a humorous story line. This was very appealing to my oldest, an avid reader. Each section tells part of the life of Fred Gauss,  a five year old who teaches math at KITTENS University in Kansas.  The story shares how, in the course of his life, Fred encounters the need for the math and then learns the methods.

As she progressed through the books, she gradually transitioned away from direct instruction whereby I was teaching concepts to her and began to rely more on her own reading. She became an independent learner.

Never again hear the question which many math students proclaim: “When are we ever gonna use this stuff?” or “Math is boring!”

Life of Fred makes this possible not only through story but with tons of solved examples. Each hardcover textbook contains ALL of the material – more than most instructors cover in traditional classroom settings.

We meet with Fred daily and have really enjoyed his adventures. I thought I’d share our experience with Life of Fred since people often have a lot of questions about it.

What I Love About Life of Fred Math Curricula

I love the story nature of the text and real life problem approach. Fred encounters a need for the math and then uses it, usually within the context of a humorous situation.

It encourages a different approach to attacking a problem. Students are encouraged to think.

Less drill and more complex problems. This lessens boredom and fatigue and leads to increased accuracy.

The texts are non-consumable; I can use them with both kids. I’ve never been a fan of workbooks; I love that they work out the problems on ordinary notebook paper.

The cost is budget friendly. The middle school texts are just $17 and the high school texts start at just $28 at Educents. You can’t go wrong even if you just wanted to try it out.

 

math curriculaLife of Fred Math Curricula for Middle School 

My kiddos had completed the Singapore Math curricula series for elementary and middle school, so this is where we actually started. They were immediately hooked on Fred’s story and have loved to read about his humorous antics.

Once you know:

  • the addition tables
  • the subtraction tables
  • the multiplication tables
  • long division

… you are ready to start Life of Fred Fractions, the first book in the Pre-Algebra series.

Who is it for? 5th – 9th grades

Concepts covered: Savings and Expenses, Sectors, Comparing & Reducing Fractions, Roman Numerals, Least Common Multiples, Improper Fractions, Commutative Law, Decimals, Functions and Inverse Functions, Pi, Sets and Subsets, Union and Intersection of Sets, Rules of Divisibility, Bar Graphs & Pie Charts, Prime and Composite Numbers, Consecutive Numbers, the Goldbach Conjecture, Conversion between Percents/ Fractions/ Decimals, Square Roots, Ratio, Ordered Pairs, Negative Numbers, Elapsed Time, Probability, and more!

Titles in this series:  Fractions, Decimals & Percents, Pre-Algebra with Physics, Pre-Algebra with Biology, Pre-Algebra with Economics

Buy Now

LifeofFred Math Curricula

Life of Fred Math Curricula for High School 

My kiddos were already familiar with Fred’s style and approach to problem solving as they had previously completed the Pre-Algebra series.  They loved that they weren’t required to do a bunch of drill-and-kill problems. When they struggled with a concept, they simply re-read the chapter.

My daughter is currently using the Advanced Algebra text. When she was about mid-way through the text, she actually made the decision herself to begin it again. We had been doing a lot of traveling and she hadn’t been going through the lessons regularly. Repeating the textbook helped to clarify the concepts that were previously foggy for her or that she didn’t recall from earlier readings.

If you …

  • have finished the Life of Fred Pre-Algebra books
  • have used another algebra program
  • have used Saxon Math Algebra 1 and/or 2

… you are ready to start the first book in the high school series, Beginning Algebra.

Concepts covered: Division by Zero, Venn Diagrams, Cramer’s Rule, Inequalities, Imaginary Numbers, Variation, Laws of Exponents, Four-dimensional Geometry, Non-Euclidean Geometry, Sines, Cosines and Tangents, Conditional Trig Equations, Functions of Two Angles, and much more!

Titles in this series:  Zillions of Practice Problems: Beginning Algebra

Buy Now

 

Building Tetrahedron Kites

Few things capture the spirit of spring like flying a kite. Watching a kite dance and sail across the sky is not only a visually appealing experience, it also provides a foundation for studies in aerodynamics – a discipline that beautifully integrates science and mathematics.  Building tetrahedron kites combines art and handcrafts as well.

The Science of Kites

A kite is a tethered aircraft that flies when the forces of lift and thrust are greater than the forces of drag and gravity.  In between flying and crashing to the ground are a variety of swoops, wiggles, pitches, yaws, and rolls that show the kite is seeking a balance among the conflicting forces.

A kite creates a physical obstacle to the normal airflow which causes the air to change direction and speed. The air flows across one surface faster than it moves across the other side of that surface. This difference in speeds results in lift in the direction of the surface with faster moving air. As air pressure can be altered by changing the kite’s angle of attack, the changes in air speed result in changes in air pressure, which cause the kite to produce greater lift.

Constructing a Kite

Begin by constructing a pyramid composed of equilateral triangles by running string through three straws, arranged in a triangle.  Continue on with the string through two additional straws, forming an additional triangle (the two triangles now share the same base).  Finally, run the string through one more straw and lift the left triangle upward to form a pyramid, tying the the lead end of the strings.

tetrahedron template

Use the template pictured here to cut out a tissue-paper covering for two sides of the tetrahedron. The template measurements are for standard length drinking straws.  Cover only two sides of the tetrahedron.  Glue the covering over the frame, wrapping the excess materials around the straw frame.  Repeat these steps to create a total of four tetrahedrons.

More detailed instructions for building these kites can be found at Easy Kitemaking: How to Build a Pyramid Kite.

triangular kite

Designing an Experiment

Now that you have familiarized yourself with the characteristics of the tetrahedron kite, design an experiment to determine how changing one variable in the kite’s design will affect its performance.

For example, you may wish to build a kite using heavier tissue paper or a different kind of covering altogether (newspaper, plastic wrap, or aluminum foil for example).  You may try a kite with a larger number of tetrahedron cells (16 instead of 4).