About a month ago, I asked for readers to submit science and math catechisms which they used in class. Today, I am happy to share a few of the many responses I received. I am happy to say that math and science teachers submitted their catechisms, but it seems coaches are employing catechisms, as well.
I hope the following collection of catechisms is helpful to math and science teachers looking for ideas.
Antiquities Algebra Catechism by Amanda Norton, Liberty Classical Academy
Why should we seek virtue?
For we know that since Christ was raised from the dead, he cannot die again; death no longer has mastery over him. The death he died, he died to sin once for all; but the life he lives, he lives to God. In the same way, count yourselves dead to sin but alive to God in Christ Jesus. Therefore do not let sin reign in your mortal body so that you obey its evil desires. Do not offer any part of yourself to sin as an instrument of wickedness, but rather offer yourselves to God as those who have been brought from death to life; and offer every part of yourself to him as an instrument of righteousness. For sin shall no longer be your master, because you are not under the law, but under grace….As obedient children, do not conform to the evil desires you had when you lived in ignorance. But just as he who called you is holy, so be holy in all you do; for it is written: “Be holy, because I am holy.”
(Romans 6, 1 Peter 1)
What is algebra?
Algebra is the branch of mathematics that uses mathematical symbols and statements to describe relationships between things that vary. It is the art of reasoning about relations and is the unifying thread of all mathematics.
Why do we study arithmetic?
Arithmetic has a very great and elevating effect, compelling the mind to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument. ….And here is another point, that those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the slow-witted if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been…arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up. (Plato Republic VII)
When will I ever need this in real life?
What sort of knowledge is there which would draw the soul from becoming to being?
But what branch of knowledge is there… which is of the desired nature; since all the useful arts were reckoned mean by us?….then we shall have to take something which is not special, but of universal application…A something which all arts and sciences and intelligences use in common, and which every one first has to learn among the elements of education. ..The little matter of distinguishing one, two, and three –in a word, number and calculation: –do not all arts and sciences necessarily partake of them? ..Can we deny that a warrior should have a knowledge of arithmetic? Certainly he should, if he is to have the smallest understanding of military tactics, or indeed, I should rather say, if he is to be a man at all… It appears to me to be a study of the kind which we are seeking, and which leads naturally to reflection, but never to have been rightly used; for the true use of it is simply to draw the soul towards being. (Plato, Republic VII)
Which operations are commutative?
The Commutative Property allows numbers to be added or multiplied in any order:
Commutative Property of Addition states that A + B = B + A
Commutative Property of Multiplication states that A * B = B * A
Which operations are associative?
The Associative property allows addition and multiplication terms to be grouped together in different ways.
Associative Property of Addition states that (A + B) + C = A + (B + C)
Associative Property of Multiplication states that (AB)C = A(BC)
What is the distributive property?
The Distributive Property states that A(B + C) = AB + AC
What are the identity properties?
The Additive Identity Property is A + 0 = A
The Multiplicative Identity Property is A * 1 = A
What are the inverse properties?
The Additive Inverse Property is A + (-A) = 0
The Multiplicative Inverse Property is A * 1/A = 1, A≠0
How is the slope of a line determined?
Slope is the description of the amount of slant of a line. It is found by the change in the y-values divided by the change in x-values between two points on a line. The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.
How do we describe numbers and their relationships?
Addends are added to find their sum.
A subtrahend is subtracted from a minuend to find their difference.
Factors are multiplied to find their product.
A dividend is divided by a divisor to find the quotient.
What is the quadratic formula?
The quadratic formula states that the solutions to the quadratic equation ax2 + bx + c = 0 are
Why should we struggle with math when the answers are on the internet?
We live in a fallen world marked by discord but with hope of all things being renewed into unity with the Creator. Struggle with unanswered problems teaches us to tolerate discord with the hope of a solution. We do not give in to despair but through struggle develop the virtues of humility, endurance, perseverance, and patience. “[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.” (Galileo) It is worth our time and effort.
What does Coram Deo have to do with Math?
Coram Deo means “before the face of God.” He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son (Colossians 1) that we may walk before God [coram Deo] in the light of life (Psalm 55:13). We do all things, including math, in the presence of God, under the authority of God, to the glory of God. We come before God in humility and repentance seeking knowledge and understanding to know him, enjoy him forever, and bring him glory.
Chemistry Catechism for Melissa Kennedy, homeschool co-op
The Lord’s Prayer
Acts 17:22-31: So, Paul, standing in the midst of the Areopagus, said: “Men of Athens, I perceive that in every way you are very religious. For as I passed along and observed the objects of your worship, I found also an altar with this inscription: ‘To an unknown god.’ What therefore you worship as unknown, this I proclaim to you. The God who made the world and everything in it, being Lord of heaven and earth, does not live in temples made by man, nor is he served by human hands, as though he needed anything, since he himself gives to all mankind life and breath and everything. And he made from one man every nation of mankind to live on all the face of the earth, having determined allotted periods and boundaries of their dwelling place, that they should seek God, and perhaps feel their way toward him and find him. Yet he is actually not far from each one of us, for “ ‘In him we live and move and have our being’; as even some of your own poets have said, “ ‘For we are indeed his offspring.’ Being then God’s offspring, we ought not think that the divine being is like gold or silver or stone, an image formed by the art and imagination of man. The times of ignorance God overlooked, but now he commands all people everywhere to repent, because he has fixed a day on which he will judge the world in righteousness by a man whom he has appointed; and of this has given assurance to all by raising him from the dead.”
What is chemistry? Chemistry is the study of elements, how they combine to form mixtures and compounds, the properties of these substances, and the processes involved. (General Chemistry by John D. Mays)
What are some fundamental principles of chemistry? Chemistry is all about electrons; chemistry is all about electrical forces; chemistry is all about minimizing energy; chemistry is all about whole-number ratios of atoms; and chemistry is all about modeling. (General Chemistry by John D. Mays)
What place does chemistry occupy in the whole of education? Chemistry resides in the realm of natural philosophy, built upon the foundation of the Trivium and Quadrivium, and taught alongside divine and moral philosophy.
What is the Trivium? The Trivium is the threefold curriculum of the language arts through the means of grammar, logic, and rhetoric. (The Liberal Arts Tradition by Kevin Clark and Ravi Scott Jain) The Trivium prepares us to study the Quadrivium by tutoring the reason and training the mind in virtue.
What is the Quadrivium? The Quadrivium is the fourfold curriculum of the mathematical arts through the means of arithmetic, geometry, music, and astronomy. The Quadrivium prepares us to contemplate God in an orderly fashion, to take delight in the source of all truth, beauty, and goodness. (The Liberal Arts Tradition by Kevin Clark and Ravi Scott Jain)
What is philosophy? Philosophy is the love of wisdom, in which we love and submit to life as it really is. This reality is threefold- God the Creator, man made in His image, and the cosmos as His creation. (The Liberal Arts Tradition by Kevin Clark and Ravi Scott Jain)
What are the divisions of philosophy? The divisions of philosophy are divine philosophy, moral philosophy, and natural philosophy. Divine philosophy is devoted to comprehending the eternal and spiritual truths. Moral philosophy is devoted to comprehending man as God’s image, both in his being and his relationships. Natural philosophy is devoted to comprehending and exploring natural causes in the realm of nature, God’s creation. (The Liberal Arts Tradition by Kevin Clark and Ravi Scott Jain)
What is the goal of natural philosophy? The study of natural philosophy leads from wonder to wisdom and results in man submitting himself in imitation and awe of the wisdom innate in nature. (The Liberal Arts Tradition by Kevin Clark and Ravi Scott Jain)
What does Athanasius say about order? Concerning order, Athanasius writes, “But if the world is founded on reason, wisdom, and science, and is filled with orderly beauty, then it must owe its origin and order to none other than the Word of God.”
General Science Catechism, by Michael Price of Westminster Academy
What is science? Science is the study of God’s world and all it contains.
Where does the word “science” come from? The word “science” comes from the Latin word scientia, which means “knowledge.”
How do we gain knowledge of God’s world? We gain knowledge of God’s world through observation and experimentation.
How should we approach God’s world? We should approach God’s world with humility and wonder, for our God is “a great God and a great King among all gods. In His hand are the depths of the earth; the heights of the mountains are His also. The sea is His, for He made it, and His hands formed the dry land.” (Psalm 95:3-5)
Do we learn about God when we study God’s world? Yes! When we study God’s world, we learn about God’s “invisible attributes, namely, His eternal power and divine nature, [which] have been clearly perceived, ever since the creation of the world, in the things that have been made.” (Romans 1:20)
Who is the true student of God’s world? The true student of God’s world is the one who bows down in worship before the Lord our Maker. (Psalm 95:6)
To whom belong all glory, honor, majesty, dominion, and power for all He has done and will do in His works of creation and re-creation? All glory, honor, majesty, dominion, and power belong to the Lord our God.
“Come, let us bow down in worship, let us kneel before the LORD our Maker.” Psalm 95:6
Who is the true student of God’s world? The true student of God’s world is the one who BOWS DOWN in worship before the LORD our Maker.
1. Be Kind to Others
2. Obey Cheerfully and Immediately
3. Work Diligently
4. Speak Honestly Laboratory Rules
1. Do use scientific equipment only in the manner intended.
2. Observe your surroundings and move carefully. Running is not allowed in the science room.
3. Wait to touch equipment until instructed to do so.
4. Never leave your work area messy. Clean up immediately and stay tidy.
Physics Catechism by Jim Dolas of Heritage Preparatory
What is our duty toward God?
Saint Paul wrote in his first letter to the church at Corinth, “So now faith, hope, and love abide, these three; but the greatest of these is love.”
Following Paul, Saint Augustine wrote, “As to virtue leading us to a happy life, I hold virtue to be nothing else than perfect love of God. For the fourfold division of virtue I regard as taken from four forms of love. For these four virtues (would that all felt their influence in their minds as they have their names in their mouths!), I should have no hesitation in defining them: that temperance is love giving itself entirely to that which is loved; fortitude is love readily bearing all things for the sake of the loved object; justice is love serving only the loved object, and therefore ruling rightly; prudence is love distinguishing with sagacity between what hinders it and what helps it. The object of this love is not anything, but only God, the chief good, the highest wisdom, the perfect harmony. So we may express the definition thus: that temperance is love keeping itself entire and incorrupt for God; fortitude is love bearing everything readily for the sake of God; justice is love serving God only, and therefore ruling well all else, as subject to man; prudence is love making a right distinction between what helps it towards God and what might hinder it.”
What is our duty toward others?
The Gospel of John tells us, “When [Jesus] had washed their feet and put on his outer garments and resumed his place, he said to them, ‘Do you understand what I have done to you? You call me Teacher and Lord, and you are right, for so I am. If I then, your Lord and Teacher, have washed your feet, you also ought to wash one another’s feet. For I have given you an example, that you also should do just as I have done to you. Truly, truly, I say to you, a servant is not greater than his master, nor is a messenger greater than the one who sent him. If you know these things, blessed are you if you do them.’”
What is our duty toward scholarship?
“The greatest error of all the rest is the mistaking or misplacing of the last or farthest end of knowledge: for men have entered into a desire of learning and knowledge, sometimes upon a natural curiosity and inquisitive appetite; sometimes to entertain their minds with variety and delight; sometimes for ornament and reputation; and sometimes to enable them to victory of wit and contradiction; and most times for lucre and profession; and seldom sincerely to give a true account of their gift of reason, to the benefit and use of men…, for the glory of the Creator and the relief of man’s estate.”
(Sir Francis Bacon, The Advancement of Learning)
What is the purpose of science?
“Philosophy is written in this great book which is continually open before our eyes–I mean the universe–but before we can understand it we need to learn the language and recognize the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a word of what it says. Without these, it is just wandering aimlessly in a baffling maze.” (Galileo, The Assayer from Selected Writings)
How can we study science?
“Since this is so, and since moreover it is clear that two truths can never contradict each other, it is the duty of the wise expositor to seek out the true meanings of Scripture which agree with those scientific conclusions which observation or necessary demonstrations have already established as certain. I would go further and argue that since, as we have seen, the Scriptures, albeit inspired by the Holy Spirit, often allow interpretations far removed from their literal meaning, for the reasons given above, and since moreover there is no guarantee that all interpreters are divinely inspired, it would be prudent not to allow anyone to use Scripture to uphold as true any scientific conclusions which observation and necessary demonstration might show to be false. For who would wish to place limits on human understanding, or claim that we already know all that there is to be known?” (Galileo, Letter to Don Benedetto Castelli from Selected Writings)
Why do we study science?
David wrote in Psalm 36: Your steadfast love, O LORD, extends to the heavens, your faithfulness to the clouds. Your righteousness is like the mountains of God; your judgments are like the great deep; man and beast you save, O LORD.
What is the discipline of physics?
“But since the manual arts are applied especially to making bodies move, geometry is commonly used in reference to magnitude, and mechanics in reference to motion. In this sense rational mechanics will be the science, expressed in exact propositions and demonstrations, of the motions that result from any forces whatever and of the forces that are required for any motions whatever.” (Sir Isaac Newton, The Principia)
Who made notable contributions to physics?
The following people made important contributions to the discipline of physics.
Democritus (5th century BC) was an ancient Greek natural philosopher who proposed that all matter was made from tiny, indivisible particles, from which we get the term “atom”.
Aristotle (4th century BC) was one of the most influential ancient Greek philosophers whose ideas about the physical universe were authoritative for almost 2,000 years.
Nicolaus Copernicus (1473-1543) was a Polish astronomer who first developed the heliocentric model of the solar system. His controversial work was published after his death in 1543.
Tycho Brahe (1546-1601) was an astronomer and nobleman from Denmark. In 1563 he observed a conjunction between Saturn and Jupiter, which he had predicted using Copernicus’s model. In 1572 he observed a nova (literally “new”), suggesting that the heavens were not fixed and eternal as Aristotle had suggested.
Johannes Kepler (1571-1630) was a German astronomer and mathematician. He worked at Tycho’s observatory in Prague, where he used Tycho’s research data to develop his three laws of planetary motion, the first two published in 1609 and the third in 1619. He modified Copernicus’s model such that the orbits of the planets were ellipses rather than perfect circles.
Galileo Galilei (1564-1642) was an Italian mathematician and astronomer from Florence. In 1610, he used a telescope he had developed to discover four moons orbiting Jupiter, the findings of which he published as A Sidereal Message. His support for the Copernican theory led to his house arrest after his trial in 1633. Galileo’s experiments on force and motion, including his discovery that all objects fall at the same rate regardless of mass, cast even more doubt on Aristotle’s ideas and set the stage for Isaac Newton.
Sir Isaac Newton (1643-1727) was an English mathematician, scientist, and philosopher. His work Principia Mathematica, first published in 1687, became the foundational text for the study of physics. Among his many accomplishments, he developed calculus, a branch of mathematics; formulated a law of universal gravitation; and developed three laws of motion.
Alessandro Volta (1745-1827) was an Italian nobleman, physicist, and chemist. Volta developed the first voltaic pile, a chemically-powered precursor to modern batteries, in 1800.
John Dalton (1766-1844) was an English chemist, physicist, and meteorologist. He developed the first scientific model of the atom. Even though there have been many new discoveries, his model is fully or partially correct in all its propositions.
André-Marie Ampère (1775-1836) was a French scientist who showed that wires that carried an electric current behaved like magnets. He developed a mathematical model relating current to the strength of the magnetic field, now known as Ampère’s Law.
Michael Faraday (1791-1867) was an English scientist. As a child he was apprenticed to a bookseller, where he read many books on physics and chemistry. Faraday was given a position in the lab of Sir Humphry Davy, one of the most respected scientists of the time, where he performed research in chemistry, electricity, and magnetism. In 1831, Faraday discovered an inverse effect to Ampère’s Law, that a magnetic field can induce an electric current in a nearby conductor, now known as Faraday’s Law of Magnetic Induction.
James Clerk Maxwell (1831-1879) was a Scottish theoretical physicist who built on Faraday’s work. In 1864 he published a complete description of all known electrical and magnetic phenomena in the universe, which can be summarized on four simple equations.
Dmitri Mendeleev (1834-1907) was a Russian chemist who discovered many patterns in the properties of the elements, leading to the development of the modern Periodic Table of the Elements in 1869.
J. J. Thomson (1856-1940) was an English scientist who discovered the electron in 1897. The electron is a tiny, negatively charged subatomic particle that is part of atoms. He developed a “plum pudding” or “watermelon” model of the atom, in which electrons were embedded in the positively charged material of the rest of the atom.
Robert Millikan (1868-1953) was an American scientist who discovered the charge on a single electron in his famous oil drop experiment of 1911. In this experiment, droplets of oil fell between two charged metal plates, picking up electrons as they went. By adjusting the strength of the electric field between the plates, Millikan could cause the droplets to hover, allowing him to determine the charge of an electron.
Ernest Rutherford (1871-1937) was a physicist from New Zealand who developed the famous gold foil experiment, in which alpha particles from radioactive decay were shot at a piece of gold foil. The behavior of the alpha particles led Rutherford to determine that the positive charge of an atom was concentrated in the nucleus, and that atoms were mostly empty space.
Albert Einstein (1879-1955) was a German physicist who famously developed the general theory of relativity, published in 1915. His theory explained gravity in terms of the curvature of space and time. He predicted that light would bend around massive objects, such as stars, a hypothesis that was confirmed during the solar eclipse of 1919.
James Chadwick (1891-1974) was an English physicist who worked with Ernest Rutherford, He discovered the neutron, a neutrally-charged subatomic particle that contributes as much mass as a proton to the nucleus, in 1932.
Niels Bohr (1885-1962) was a physicist from Denmark who, along with Ernest Rutherford, developed a “planetary model” for atoms in 1913, in which electrons orbited the nucleus in specific orbits with specific amount of energy, and gaining or losing energy would move an electron further from or closer to the nucleus. His model led to the development of the modern quantum understanding of the atom.
What are the equations of physics?
(GIBBS NOTES: Due to formatting issues, what follows is not exactly what the catechism includes. The equations listed below have been copied from a Google Doc and pasted into Word, which has significantly altered them. I take it that experienced math and science teachers know how to interpret the following.)
We use the following equations to model physical phenomena:
Constant velocity: v=dt
Uniform acceleration: a=(vf -vi)t
Newton’s Second Law of Motion: a=Fm
Gravitational potential energy: EG=m•g•h
Kinetic energy: Ek=12m•v2
Velocity as a function of kinetic energy: v=2Ekm
Pressure under a liquid: P=•g•h
Pressure as force applied in an area: P=FA
Wave equation: v=•f
Period of a wave: =1f
Ohm’s Law: V=I•R
Electrical power: P=V•I
What are Kepler’s Laws of Planetary Motion?
Kepler’s Laws of Planetary Motion are summarized as follows:
“First Law: The orbit of a planet is an ellipse with the Sun at one of the two foci.
Second Law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Third Law: The square of a planet’s orbital period is proportional to the cube of the length of the semi-major axis of its orbit.”
What are Newton’s Laws of Motion?
Sir Isaac Newton summarized his laws of motion in the Principia:
“Law 1: Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed.”
“Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.”
“Law 3: To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction.”
What is the general theory of relativity?
Albert Einstein wrote in Relativity, “We wish to understand by the ‘general principle of relativity’ the following statement: All bodies of reference, K, K’, etc., are equivalent for the description of natural phenomena (formulation of the general laws of nature), whatever may be their state of motion.” Or, more generally, “All Gaussian co-ordinate systems are essentially equivalent for the formulation of the general laws of nature.”
What does it mean that energy is conserved in a system?
“It follows thence that the total quantity of all the forces capable of work in the whole universe remains eternal and unchanged throughout all their changes. All change in nature amounts to this, that force can change its form and locality without its quantity being changed. The universe possesses, once for all, a store of force which is not altered by any changes of phenomena, can neither be increased nor diminished, and which maintains any change which takes place on it.” (Hermann von Helmholtz, On the Conservation of Force, translated by Edmund Atkinson)
What is the mechanical equivalent of heat?
James Joule wrote, “That the quantity of heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity of force expended.”
Girls Basketball Catechism by Kevin Farmer of Bloomingdale Public Schools
Who are you?
We are queens of the court. We rule our kingdom with grace, love, truth, and an Iron Resolve.
What is your Goal?
In the words of Kobe Bryant: The important thing is that your teammates have to know you are pulling for them and you really want them to be successful.
How do you win?
MJ says, “I have always believed that if you put in the work, the results will come. If you do the work, you get rewarded, there are no shortcuts in life.”
What is a team?
When you can’t run, you walk.
If you can’t walk, you crawl.
And if you can’t crawl, you find someone to carry you.
What is a teammate?
Teamwork is what makes common people capable of uncommon results. -Pat Summit
What is success?
Coach Wooden says, “Success is peace of mind which is a direct result of self-satisfaction in knowing you made the effort to become the best you are capable of becoming.”
Why do we play?
Mia Ham tells us: “Somewhere behind the athlete you’ve become and the hours of practice and the coaches who have pushed you is a little girl who fell in love with the game and never looked back… play for her.”
Math Litany by Syra Ruehle
What is the Substitution property of equality?
If a equals b, then a can be substituted in for b in any expression. Substitution.
What is the Reflexive Property of Equality?
A number is equal to itself. a=a “a equals a.” Reflective Property of Equality.
What is the Symmetric Property of Equality?
If one number is equal to a second number, then the second number is equal to the first number. If x=y then y=x “If x equals y, then y equals x.” Symmetric Property of Equality.
What is the Transitive Property of Equality?
If we have two equal values and either of those values is equal to a third value, all the values must be equal. If a=b and b=c, then a=c. “If a equals b and b equals c, then a equals c.” Transitive Property of Equality
What is the Commutative Property of Addition?
The order of the terms in a sum doesn’t change the result. a+b=b+a “a plus b equals b plus a.” Commutative Property of Addition
What is the Commutative Property of Multiplication?
The order of the factors in a product doesn’t change the result. a∙b=b∙a “a times b equals b times a.” Commutative Property of Multiplication.
What is the Associate Property of Addition?
The sum of three or more numbers remains the same regardless of how the numbers are grouped. (a+b)+c=a+(b+c) “The quantity a plus b all plus c is equal to a plus the quantity b plus c.” Associative Property of Addition.
What is the Associative Property of Multiplication?
The product of three or more factors remains the same regardless of how the numbers are grouped. (a∙b)∙c=a∙(b∙c) “The quantity a times b, all times c is equal to a times the quantity b times c.” The Associative Property of Multiplication
What is the additive identity?
The additive identity is zero because adding zero to any value will leave the value unchanged. a+0=0+a=a “a plus zero equals zero plus a equals a.” Additive identity.
What is the multiplicative identity? The multiplicative identity is one because multiplying any value by one will leave the value unchanged. a∙1=1∙a=a “a times one equals a times 1 equals a.” Multiplicative identity.
Geometry Catechism by Greg Wilbur of New College Franklin
Why do we study Geometry?
We study geometry because Yahweh has revealed Himself in the things that He has made, all creation sings His praises, and number is the language of creation.
Who are you?
I am a vice-regent of the Creator entrusted to rule, tend, and cultivate the cosmos as a sub-creator, to bring harmony to discord, and to be an agent of shalom.
What is number?
Number is a divine symbolic language that can be used to describe the created order of the cosmos which is upheld by Christ by the word of His power.
Is Mathematics created?
Mathematics is discovered, not created.
What is the Quadrivium?
The Quadrivium is the study of the language of creation through the means of arithmetic, geometry, music, and astronomy.
What is Arithmetic, Geometry, Music, and Astronomy?
Arithmetic is number and the meaning of numbers. Geometry is number in relationship. Music is number in relationship in time. Astronomy is number in relationship in time and space.
What is a point?
A point is that which has no part and represents the monad.
What is a line?
A line is breadthless length and represents the dyad.
What is a surface or plane?
A surface or plane has length and breadth only and represents the triad.
What is a solid?
A solid has length, breadth, and depth and represents the tetrad.
What is the love of Christ?
The love of Christ has “breadth and length and height and depth,” it surpasses knowledge, and represents the fullness of God.
What are the Four Contraries?
The Four Contraries are: hot (summer), cold (winter), wet (autumn), dry (spring).
What are the Four Sublunary Elements?
The Four Sublunary Elements are Fire, Air, Water, and Earth.
What are Platonic Solids?
Platonic Solids are three-dimensional shapes consisting of congruent faces in which all angles and sides are equal and such that the same number of polygonal faces meet at each vertex.
How many Platonic Solids are there?
There are five Platonic Solids: the tetrahedron, the octahedron, the icosahedron, the hexahedron, and the dodecahedron.
What is the Sacred Tetractys? The Sacred Tetractys, or Plato’s Lambda, is comprised of the Monad, the first even and odd, the first even and odd squares, the first even and odd cubes.