Just for a moment, reflect on what you did from the time you awoke. Is there anything among what you did that does not have at least the slightest connection to mathematics? There can hardly be any. Our life is unknowingly attached to mathematics in almost all ways. Whatever we do, we have to use math. No matter what the field that we are employed in, we get to use math. Simply, it’s the same with carpentry as well. The impact of mathematics in carpentry is amazing!
In fact, we need mathematics in the fields of construction, security, education, business, health, and communication. The methods we use it and the extent up to which we use it can be different. Yet, math is always the root of any primary concept that we use in each of those fields. All other theories and factual knowledge depend on the basics of mathematics. Unquestionably, any other subject field is a subsection of math. Mathematics is the lifeblood of nature as a whole.
The field of construction uses math in it more than in most other fields. You might get the feeling that mathematics is a subject that deals with absurd formulas and functions. Actually, it’s not. The ultimate result of all the maneuvers is to make our lives easier. The theoretical knowledge of mathematics helps us in our day-to-day life in distinct matters. In the concrete, you might not even be aware of how math pokes its nose into all these affairs. But it has an inevitable but priceless impact. In spite of all the subsections of the field of construction, carpentry is significant in this regard for it deals with mathematics more than in any other. Hence, let’s get to know about the wonderful impact of mathematics in the field of carpentry.
The Role of Mathematics in Carpentry
Undeniably, the role of mathematics in the field of carpentry is foremost. Just see for yourself woodwork. Scrutinize how much math they have used! This doesn’t mean at all that you have to be a modern-day Einstein to indulge yourself in carpentry. Sometimes, you might be a very talented carpenter. Maybe you know for yourself that you weren’t pretty good at math in school. Yet, you keep growing in your profession. You use mathematics in all that you do in carpentry. But you don’t know that you do so. However, you would find it fascinating to find out the influence of mathematics in carpentry through this article.
In actual fact, all the knowledge a carpenter possesses on concepts of mathematics is most likely common sense. Over the course of time, they become habitual practices. If you are an experienced carpenter, maybe you might not know about such theories by name, but you know what it says and how you should use it. You have gotten that profound proficiency simply due to your work experience.
The primary stage of any carpentry job is the measurement. It is the instance where mathematics plays the first key role in carpentry. Afterward, you may have to think of a simple design or a plan to work on your task. That’s another occurrence that mathematics has an influence on carpentry. Even within the execution of your plan, you need to use your basic mathematical knowledge. Going further, even a neat finishing requires a good mathematical wit. But you don’t have to be a math prodigy to excel in the field of carpentry.
Mathematics in Carpentry Applications
No doubt you would be curious to know about the influence of mathematics on the field of carpentry in detail. Manifestly, there are few distinct ways that a carpenter has to cope with mathematics. They belong to various stages and ways of production. Indeed, you can use your mathematical cognition to make your work more efficient and easier. The main objective of this article is to give you a clear idea about how you should utilize the relationship between mathematics and carpentry in a much fruitful manner. Let’s consider the following.
- The Basic Concepts of Mathematics that a Carpenter needs to know
- Measurements of carpentry
- How to make Carpentry work more profitable with the use of Mathematics?
- Use of Mathematics to increase the quality of your work
- Efficiency through the use of Mathematics
Beyond doubt, you must be anxious to know about all those. Keep reading! There’s so much you have to know about mathematics in carpentry.
1. The Basic Concepts of Mathematics that a Carpenter needs to know
Seemingly, there are some primary concepts and theories of mathematics that a carpenter must know. It is not a must that you should learn all these by books. Conceivably, many carpenters master these theories by experience. Even if you learn these by books, you might not clearly know about applying them in your carpentry work. Hence, on most occasions, it is mostly your experience that helps you.
Substantially, some main skills of mathematics like geometry, arithmetic, and algebra help you in carpentry. At times, you might find it useful to know basic trigonometry also. There are certain occasions that require complex mathematical knowledge of calculus. Yet, the basic mathematical theories that have an interrelation with carpentry are worth knowing descriptively.
a) Basic arithmetic in carpentry
b) How carpentry uses Geometry
c) Use of calculus in carpentry
d) Statistics in carpentry
Henceforth, you will be able to know about all that from top to bottom. Calm your anxiety! Keep reading!
a) Basic Arithmetic in carpentry
In point of fact, we need to use basic arithmetic in almost all that we do in our lives. Besides, carpentry being a profession that tackles measurements in most cases deals with arithmetic to a great extent. The arithmetic principles that are requisite in carpentry are actually the most primary concepts. Needless to say, even a kid knows the basic arithmetic concepts that a carpenter has to interact with.
What are the basics of arithmetic? Addition, subtraction, multiplication, and division are the major subdivisions of basic arithmetic. Irrespective of the profession, anyone has to deal with them under different circumstances. A carpenter’s work with these basic arithmetic concepts is much higher in quantity, though.
Fundamentally, you will have to add and subtract different values when you are getting your measurements. Perhaps, you may have to get the total length of some item. Then you have to add each length that you measure. The use of subtraction is alike. Further, you may have to calculate the total length or area of a set of similar items. Then you surely will have to multiply one’s length or area by the number of items you have. Assume that you have to calculate the total cost of the paint that you use in your wood product. If you know the cost of the paint per unit area of your item, you can estimate the total cost for the paint by multiplying it from the surface area.
In such ways, you get to use simple arithmetic in your carpentry work. To make the calculations convenient, you can use a pocket calculator.
b) How carpentry uses geometry
Geometry is a field of mathematics that is so very connected with carpentry. From the distant past, people preferred symmetry in objects. That is the primal stage that people used geometry. If you go take a look at some ancient palace, you will see the geometrical knowledge people have used in the days of yore. You can use the knowledge of geometry to preserve the symmetry of objects even in your trade. Moreover, you definitely have to use geometry on the grounds of your convenience, or to produce a durable and quality product. Here are two main concepts that you will have to use prominently in carpentry.
- Pythagorean Theorem
- Calculation of areas and volumes
You surely would like to know in-depth about all these. Nothing to worry about, you probably will!
Pythagorean Theorem
Pythagorean Theorem is a theorem that every carpenter should definitely know. Let’s move to a full overview of the Pythagorean Theorem and its impact on carpentry.
The origin of the Pythagorean Theorem
It is quite uncertain whether a particular individual discovered this Principle or a group was involved. Historians say that this concept has been in the world at different times in distinct places. However, saying that the Greek Mathematician Pythagoras discovered this Theorem considering its name is a highly arguable assumption. Some say that Babylonian mathematicians had discovered and proved this Theorem about a millennium before the birth of Pythagoras. Anyway, the contribution of Pythogoros to the field of mathematics is plentiful. Therefore, it doesn’t matter who discovered the Pythagorean Theorem, naming it after him would do no harm for there is no proper evidence to prove who initially discovered it.
What does the Pythagorean Theorem say?
In the Pythagorean Theorem, it says that the area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.
Let’s assume that we have a right triangle with sides that have lengths a,b, and c where c is the length of the hypotenuse. The Theorem says a2+b2=c2. Anyway, you can even use this equation as b2=c2-a2 if you need to do the calculation that way.
Perhaps you may have heard and you may know about Pythagorean triples. What exactly is a Pythagorean triple? Well, a Pythagorean triple is a set of three positive integers that satisfy the equation a2+b2=c2 whereas a, b, and c are the positive integers. Here are some common Pythagorean triples.
- 3, 4, and 5
- 5, 12, and 13
- 7, 24, and 25
- 9, 40, and 41
- 11, 60, and 61
These are very useful in carpentry for any design. It is important that you have an idea about all these for it makes your tasks easier than you would expect them to be.
Use of Pythagorean Theorem in Carpentry
No doubt you might surely be eager to know about how you can apply the Pythagorean Theorem in carpentry work. As it happens, sometimes you may already know. But you can get to know some additional facts through this article for certain.
Usually, carpenters use the Pythagorean Theorem whenever they need to get a 90-degree angle for some purpose. This might be regarding various constructions. Perhaps, it might be regarding the construction of a wooden floor, a roof, a deck, or any other such entity. In each of those instances, you have the ability to use the Pythagorean Theorem to get the right angle.
Furthermore, when you know two sides of a right triangle, the Pythagorean Theorem helps you calculate the length of the remaining side. To get to know about the amount of some material you need for your carpentry task, you can use this method. If you are building a roof, the length of the rafter is the length of the hypotenuse of the right triangle you choose. You can then use the Pythagorean Theorem. Also, if you want to calculate the rise and run of a staircase what else except for the Pythagorean Theorem can you use?
No matter even if it’s a square. You have the ability to split the square into two right triangles. Then you know what you should do. Apply the Pythagorean Theorem to each of the triangles as per your expectation. It’s as simple as that.
Thus, maybe in installing door frames and windows or with your work related to roofs or foundations, you will have to verify the squareness of the particular object. You can use the Pythagorean Theorem for your assertion.
The Timelessness of the Pythagorean Theorem
Did you even for a moment reflect if an age-old concept in mathematics would help you ease your work in carpentry in the 21st century? Well, unquestionably, it would help carpenters from generations yet unborn even in the future. As it happens, the Pythagorean Theorem is a timeless mathematical concept. Such a concept in mathematics would help carpentry universally and timelessly.
Calculation of areas and volumes
There can be occurrences that a carpenter has to calculate the area or volume of a specific item. What are those? Just think that you have gotten a wood flooring job to carry out. What is the first thing you have to do? You would know by experience. Even if not, you can just speculate. The inceptive step of your procedure is to calculate the surface area of the floor.
What is the objective of calculating it? In fact, there are two main objectives.
- In order to estimate the cost – You certainly have to estimate the cost of your job. Your client does need that. How can you do it without calculating the surface area or the volume of what you form? Most of the time, you usually cost for the surface area or the volume of your job. Hence, it’s vital to do proper calculations.
- To estimate the amount of material that you must use – Prior to your production or reconstruction, you must know the amount of material you require. If not, you do not have the ability to at least purchase the right amount. You will be able to estimate the amount that you need only if you do the calculations right.
So, you surely will have to calculate surface areas and volumes. How are you going to do that? You have to know the formulas that you need.
Calculating Areas of fundamental shapes
Here are some fundamental shapes and formulas to calculate their surface areas.
- Square – A square is a plane figure with four straight and equal sides. The length of one side squared is the surface area of a square.
- Rectangle – A rectangle is a plane figure with four straight lines and four right angles, one with adjacent cells that are unequal. By multiplying the lengths of the unequal adjacent sides, you can calculate its surface area.
- Triangle – This is a plane figure with three straight sides. Its area is equal to one-half the product of the base and height. If there’s no accurate way to find its height, you may use Heron’s Formula. s(s – a)(s – b)(s – c)is how it goes. s in this formula is half the perimeter and a, b, and c are lengths of the sides.
- Circle – A circle is a round plane figure whose boundary consists of points equidistant from a fixed point. You can calculate the area by the formula r² where r is the radius of the circle. Further, you can calculate its circumference by the formula 2r where r is the radius.
- Trapezoid – This is a convex quadrilateral with at least one pair of parallel sides. By multiplying its height by one-half the sum of its parallel sides, you can calculate its surface area.
You can easily use the above formulas in calculating areas of basic shapes. As the surface of most solid figures consists of those fundamental shapes, you can use them accordingly to calculate their surface areas. You may use the same method even for composite plane figures that have the fundamental shapes.
Calculating areas of fundamental solid figures
You must have the knowledge of calculating the surface areas of the following solid figures also.
- Sphere – A sphere is a round solid surface with each point on its surface being equidistant from its center. To calculate the area of a sphere, you can use the formula 4r2. r is its radius.
- Cone – This is a solid figure that tapers smoothly from a flat base to a vertex. To find its area, you can use the formula r2 + rl where r is the radius of its circular base and l is the slant height.
Knowing those would ease your work. They might help you with your calculations.
Calculating Volumes
You might also have to calculate volumes of different objects in carpentry. Down below are some ways to calculate volumes of some basic solid figures.
- Prism – A prism is a polyhedron with an n-sided polygonal base, a second alike base, and n other faces joining corresponding sides of the two bases. So, even cubes and cuboids are technically prisms. To calculate the volume of a prism, you can multiply the surface area of its base by its length.
- Cylinder – Calculating the volume of a cylinder is not hard at all. All you have to do is to multiply the area of one of its circular bases by its length.
- Sphere – As for a sphere, you can use the formula 43r3 to calculate its volume. r is the radius of the sphere.
- Cone – The volume of a cone is one-third the volume of a cylinder with the same radius. So, the formula to calculate the volume of a cone is 13r2h where r is the radius and h is the height of the cone.
Thus, if you know all of them perfectly, you can become a perfect carpenter enriched with expert knowledge. Even if not, don’t worry, you can refer to some resources to find the formulas you need.
c) Use of calculus in carpentry
You might be astonished to hear that you need knowledge of calculus which is a quite advanced concept in mathematics for carpentry. It is fair enough for you to be skeptical in this regard. Maybe you are a carpenter, but you have not mastered calculus. In actual fact, you don’t need to.
Normally, the designing part of a production is done by an engineer. Also, you might work on a plan that an architect has drawn. In such cases, you don’t need to have that knowledge. You just have to work on the design. Hence, It is adequate only for the designers to have a sound knowledge of calculus. Yet, the fact that calculus is used in the complete process of carpentry is what we try to emphasize. Maybe that’s all you should know. But there’s no harm in knowing how calculus helps carpentry if you are a carpenter. These facts would delight you.
What carpentry needs prominently is differential calculus. Just think that you need to find the ideal dimensions that you should use to make a particular wooden box in a way that you can get the biggest volume using the same amount of material. That is where one can use differentiation. Using differential calculus, you can calculate the dimensions of a product to get the maximum or minimum of some specific physical quantity.
Perfecting calculus is not a major qualification of a carpenter. But if you have the knowledge, you are undoubtedly significant in your field.
d) Statistics in Carpentry
This is yet another field that a carpenter should not know in-depth. But just like calculus, it contributes to the whole process of carpentry. This is a subject field that we use to carry out a mathematical analysis of a set of data. Clearly, you don’t have to do analyses. But what you need to know is that it helps the whole process by giving you a clear idea about the expectations of people.
Statisticians collect data from people about their preferences. So, you can find information from the statisticians about people’s experiences with specific carpentry products and what people prefer. Based on the information of the statistician, you can make decisions. You can decide which carpentry products need development and which do not have a demand. Perhaps, you can even start working on new carpentry ideas.
2. Measurements of Carpentry
No doubt measurements play a major role in the field of carpentry. You have to use accurate measurements in your productions and carpentry work. Let’s take a look at the importance of accurate measurements.
Importance of measurements
“Measure twice, cut once” is something that you surely may have heard of. Measuring is a lot more important than cutting the lumber. That’s what it says. Just think that you have proceeded in your carpentry work up to some extent and then find out that your measurements are wrong. Well, by then you may have wasted a lot of costly materials and most of your precious time. But you will have to do your work again starting from the very beginning.
Thus, taking accurate measurements is apparently the most important of your woodwork. As it says in the idiom; ‘Well begun is half done’, the beginning is important. In carpentry, the beginning is even more important, simply because it is the place that you take the measurements. Inaccurate measurements can cause a lot of problems. As you may know, you may even have to restart your work.
Nevertheless, no human can measure with 100 percent accuracy. What we can do is to measure with precision. Using our measuring tools, we must measure to the smallest possible unit and we must measure more than once. It could be twice or thrice. Then, we can get a measurement precise to the smallest unit of our measuring instrument.
Measurements and carpentry
Among carpentry tools that you can use, the tape measure is the most important and most used. Even in a budget carpentry toolbox, you must have a tape measure. Also, even if you are not a carpenter by profession, a tape measure is one of the essential home tools for anybody. In most ordinary measuring tapes, you can get a reading precise to 116 of an inch or sometimes to 132 of an inch.
Other than the tape measure, the speed square, protractor, the mechanical carpenter’s pencil, and the laser measure are some carpentry tools that carpenters use nowadays.
Anyway, it is not merely the measurement that matters. You must have an idea of unit conversions also. You may have to convert the measurements you measure from one unit to another in your carpentry work. However, if you work on advanced carpentry tasks, you may sometimes have to use temperature conversions too.
Apart from what you measure, you must know about ratios. You must have the ability to understand the ratio in a plan to determine the actual scale.
Carpentry Measuring Tools
3. How to make Carpentry work more profitable with the use of mathematics?
Needless to say, you work for a maximum profit. You would surely endeavor to increase your profit. But do you know that you can use mathematics to increase your profits in carpentry? You probably can use your mathematical cognition to earn more than you would usually do.
If you are producing wood items and running a business on your own, you should be aware of the trade opportunities in your field. Then only, you will be able to produce what the customers need the most. Likewise, you can try different creative ideas to cater to your customers’ preferences based on their feedbacks. You can use the knowledge of statistics for this. If you do this, you can make more profits from your trade.
Further, you can use differential calculus in this regard. You may need to produce your products to have maximum storage if it is a wood product meant for storage. Then, you can calculate the most suitable dimensions using differentiation. Thus, your final product looks to have a very large storage. But you have used the minimum materials. Basically, it means that you can have a big profit from the item that you produced at a low cost. If you know the method, you can apply it for any of your carpentry tasks to earn the biggest possible profit.
4. Use of Mathematics to increase the quality of your work
There’s no carpenter who does not intend to produce a quality product or to perform a quality carpentry job. In fact, you can use your mathematical knowledge to make your wood products high-quality ones.
Making use of the mathematical concepts that you can use in carpentry, you can produce your products without mistakes or faults. Even after the production or your carpentry task, you can check its accuracy using the basic math concepts you know.
So, you can eventually earn a reputation as a skilled carpenter. You can use mathematics as your secret spirit for success to excel in high-quality carpentry.
5. Efficiency through the use of Mathematics
You like to save your time, don’t you? For that, you need to have efficiency in all your work. To become more efficient, you need to be unique in your carpentry work. In fact, you need to take the advantage of your math knowledge.
If you know the math concepts, you don’t really have to waste your time practically making attempts to get it right over and over again. You can perform your task then and there at the time you start doing it when you know the correct and effective method. With adequate mathematics knowledge, you can make your carpentry work much more efficient as you know how to do it at a glance. If not, you have to use your practical knowledge for some time making attempts to find the right way. Hence, if you use math, no doubt you can be an efficient carpenter.
When you are efficient, you save time. Saving time means making money. Ultimately, you see that your efficiency has brought you money.
Bottom line
The carpentry job market is so diverse, so you can excel and succeed in carpentry in different paths if you have the passion. According to The U.S. Bureau of Labor Statistics, through experience, you can go to much higher pays. With your work experience, you can master the art of carpentry to the brim. Being boastful about you without proper knowledge can result in harmful ways. Exercising prudence in mathematics sufficiently to make yourself a qualified carpenter is what you should do. Don’t limit your profession. Flounder in new seas. Even the math knowledge you have as a carpenter can take you to massive heights in carpentry.
