Vitruvian man (Bivariate data)

Vitruvian Man

What is Vitruvian man? The Vitruvian Man is a drawing made by the Italian polymath Leonardo da Vinci in about 1490. It is accompanied by notes based on the work of the Roman architect Vitruvius. The Vitruvian Man, a late 15th-century drawing, is a prime example of such work. Intended to explore the idea of proportion, the piece is part work of art and part mathematical diagram, conveying the Old Master's belief that “everything connects to everything else.

Question: Do we have the perfect body proportions in this class as per Vitruvian man 

The perfect body proportions (your wingspan is the same as your height).

Plan: Some factors that need to be controlled are making sure people aren't wearing shoes this

could lead to an increase in height and will make my measurements incorrect. I may need to

repeat measurements just to make sure that they are accurate. I will also make sure that I

measure from their longest finger to the other longest finger. 

Data: My two variables are going to be height and wingspan. My data is going to be collected from

year 11 boys in L1VO.

Q: Do we have the perfect body proportions

P: Who are the participants 

V: Variables and values

R: Relationship. What are you expecting 

S: Step by step

C: Control
C: Conditions
R: Repeat

T - Trend 

D - Direction

S - Strength 

U - Unusual outliers 

Trend: Linear 

Direction: Increasing

Strength: Moderate 

Unusual outliers: 1

In conclusion, the answer to our question (does our class have the perfect body proportion) is no the class does not have the perfect body proportion. 25% (5/20) of the class does have the perfect proportions everyone else has an uneven wingspan to height ratio.

Sawhorse Woodwork

Manufacture of a Sawhorse using Hand tools for my Building Construction  Industry Trades Organization qualification.

In term 1 2021 I learned how to use hand tools to manufacture a Saw Horse to a specific size from a set of drawings. This took about 6 weeks (24 hrs) I will explain how to make a sawhorse in this blog post

Here is my finished project.

This project was made by using hand tools only. No powered tools were used apart from a battery-powered drill to drill the holes for the screws.

I enjoyed drilling in my legs the most because it meant that I was getting closer to finishing my work

I found cutting the bottom of the legs the most difficult part because I had to get the measurements right or else my work wouldn't sit on the ground evenly. I overcame this by checking multiple times to make sure all my measurements were correct.

To make a sawhorse I carried out the following processes.

Tools I used:

Hand Saw

Chisel

Wooden Mallet

Try Square

Drills

Sliding Bevel

Marking Gauge

Plane

Combination square

For the first day or two, I was measuring my lines to cut the space where my legs would be put in. Once I marked the lines I began cutting but I couldn't cut all of it, I had to use a chisel to get the middle pieces out. Once I had finished that I needed to cut my legs out. When cutting my legs I had to cut them on an angle so that they would fit in perfectly. I then had to plane the legs down to the right angle then cut a little corner piece so they would fit. After that I needed to drill them in, most of my leg pieces fit in well. After that, I cut out the support plates and drilled them on. I then cut my support beam that goes underneath out and drilled it in and it fit well. After all that I just had to cut my feet down to size and to a flat angle so they sat flat on the ground and then I was done

• Marking out the top.

• Cutting the joints

• Hand sawing the leg ends.

• Marking out / planing the legs

• Fixing the legs

• Attaching the end piece and support.

 

Different Graphs and Their Uses

 What are the different types of graphs and their uses?

Bar Graph: A Bar Graph is used to compare things between different groups or to track changes over time. However, when trying to measure change over time, bar graphs are best when the changes are larger.

 

 

Pie graph: A pie graph can be used to show percentages. A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice is proportional to the quantity it represents. Pie charts are best to use when you are trying to compare parts of a whole. They do not show changes over time. 

 

 

Donut Graph: A donut graph is used to show the proportions of data. The donut graph was created using a count of features. Displaying values or percentages in data labels is very useful in a doughnut chart, but if you want to compare the data points side by side, you should use a stacked column or stacked bar chart instead. Consider using a doughnut chart when: You have one or more data series that you want to plot.

 

 

 

Line chart: A line chart is a graphical representation of an asset's historical price action that connects a series of data points with a continuous line. This is the most basic type of chart used in finance, and it typically only depicts a security's closing prices over time. Line graphs are used to track changes over short and long periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be used to compare changes over the same period of time for more than one group.

 

 

Scatter Graph: A scatter plot’s primary uses are to observe and show relationships between two variables. The dots in a scatter plot represent the values of the data that you have received. 

How to work out volume with different shapes

 How to work out the volume?

What do we mean by volume?

the amount of space that a substance or object occupies or that is enclosed within a container.

How do we measure it?

In math, volume is the amount of space in a certain 3D object. For example, a fish tank has 3 feet in length, 1 foot in width, and two feet in height. To find the volume, you multiply length times width times height, which is 3x1x2, which equals six. So the volume of the fish tank is 6 cubic feet.

Is there a conversion to liters?

A liter is a cubic decimetre, which is the volume of a cube 10 centimeters × 10 centimeters × 10 centimeters (1 L ≡ 1 dm3 ≡ 1000 cm3). Hence 1 L ≡ 0.001 m3 ≡ 1000 cm3 and 1 m3 (i.e. a cubic meter, which is the SI unit for volume) is exactly 1000 L.

The volume of a rectangle

To find the volume of a rectangle, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

The volume of a cylinder

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r²

The volume of a prism 

-Volume of a rectangular prism = (length x width x height) cubic units. V = (l x w x h) cubic units

The volume of a barrel

When used to denote a volume, one barrel is exactly 42 US gallons and is easily converted to any other unit of volume

The volume of a cone

The formula for the volume of a cone is V=1/3hπr²

Basic Shapes

 

Area of basic shapes

 How to find the area of a rectangle:

 

How to find the area of a triangle:  Video link-  Area of a triangle

How to find the area of a circle:

Triangle facts

Triangle Facts:

The sum of all the internal angles of a triangle is always 180o no matter how the triangle is constructed.

The length of any side of a triangle is shorter than the sum of the other two sides

A triangle can always be split into two right triangles no matter how the triangle is constructed

All triangles add up to 180°.

The 7 types of triangles: 

Equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse, and acute.

Equilateral- In geometry, an equilateral triangle is a triangle whose all three sides are of equal length.

Obtuse Scalene- An obtuse triangle is any triangle that has an obtuse angle. An obtuse angle is one that measures greater than 90 degrees. An acute angle is one that measures less than 90 degrees. A scalene triangle is one that has all three sides of a triangle of different lengths and all three angles of different measures.

Acute Scalene- As mentioned, an acute triangle consists of three acute angles (measuring less than 90 degrees), while scalene triangles contain three unequal sides and angles. Therefore, an acute scalene triangle has the following properties: Three intersecting line segments. Three acute angles. None of the sides are equal.

Right isosceles - An Isosceles Right Triangle is a right triangle that consists of two equal-length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

Obtuse isosceles - An isosceles triangle is a triangle that has at least two equal sides. So, for an isosceles triangle to be considered obtuse, it just has to be a triangle with two equal sides and an angle that is between 90 degrees and 180 degrees.

Acute Isosceles - Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

Right scalene - It has no equal sides so it is a scalene right-angled triangle. And, like all triangles, the three angles always add up to 180°

Pink Shirt day

Anti-Bullying Day is a day when people wear a pink shirt to symbolize a stand against bullying. It originated in Canada and is now celebrated on various dates around the world. The original event was organized by David Shepherd and Travis Price of Berwick, Nova Scotia, who in 2007 bought and distributed 50 pink shirts after male ninth-grade student Chuck McNeill was bullied for wearing a pink shirt during the first day of school. In Nova Scotia, Nova Scotia Premier Rodney MacDonald proclaimed the second Thursday of September "Stand Up Against Bullying Day" in recognition of these events.

I think that pink shirt day is a good idea because it shows everyone that people care about bully and that it is a problem that needs to stop

Mean, Median, Mode

Mean: The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. 

Median: The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median. 

Mode: The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.

LINK

Give one example of a practical use - where you would find it useful.

When the average income for a country is discussed, the median is most often used because it represents the middle of a group. Mean allows very high or very low numbers to sway the outcome but the median is an excellent measure of the center of a group of data.

LINK 

Is it Useful: Yes because you can use it for different measures of center in a numerical data set. They each try to summarize a dataset with a single number to represent a "typical" data point from the dataset. 

Who invented mean, median, mode.

Mean: Edmund Halley

The term is first found in the mid-1690s in the writings of Edmund Halley, and it has been used to summarize observations of a variable since the time of Galileo

Median: Antoine Augustin Cournot 

In 1843 was the first to use the term median for the value that divides a probability distribution into two equal halves.

Mode: Karl Pearson

Early use of the statistical concept of the mode was by English mathematician Karl Pearson in 1895 when he stated that “I have found it convenient to use the term mode for the abscissa corresponding to the ordinate of maximum frequency”.

When was it first used: The term is first found in the mid-1690s.

VIDEO LINK

Conversion chart mm to km

Conversion chart 

To convert mm to cm, divide the number of mm by 10 to get the number of cm.

To convert cm to m, divide the number of cm by 100 to get the number of m.

To convert m to km, divide the number of m by 1000 to get the number of km.

mm	cm	m	km
12000mm	1200cm	12m	0.012km
5000mm	500cm	5m	0.005km
1200000	120000	1200m	1.2km
326mm	32.6cm	0.326m	0.000326
1200mm	120cm	1.2m	0.0012km

  

7 basic tools in woodwork

7 basic tools in woodwork

1. Combination square: A combination square is a multi-purpose measuring and marking tool used in metalworking, woodworking. It is composed of a rule and one or more interchangeable heads that can be attached to the rule. Wikipedia. Video.

2. Sliding bevel: A sliding T bevel, also known as a bevel gauge or false square is an adjustable gauge for setting and transferring angles. Different from the square, which is fixed and can only set a 90° angle, the sliding T bevel can set any angle and transfer it to another piece. Wikipedia. Video.

3. Woodworkers try square: A try square or is a woodworking tool used for marking and checking 90° angles on pieces of wood. Though woodworkers use many different types of squares, the try square is considered one of the essential tools for woodworking.

The square in the name refers to the 90° angle. To try a piece of wood is to check if the edges and faces are straight, flat, and square to one another. A try square is so-called because it is used to try how to square the workpiece is. Wikipedia. Video.

4. Marking gauge: A marking gauge, also known as a scratch gauge, is used in woodworking and metalworking to mark outlines for cutting or other operations. The purpose of the gauge is to scribe a line parallel to a reference edge or surface. It is used in joinery and sheet metal operations. Wikipedia. Video.

5. Carpenters pencil: A carpenter pencil is a pencil that has a body with a rectangular or elliptical cross-section to prevent it from rolling away. Carpenter pencils are easier to grip than standard pencils because they have a larger surface area. The non-round core allows thick or thin lines to be drawn by rotating the pencil. Thin lines are required for high precision markings and are easy to erase, but thick markings are needed to mark on rough surfaces. Wikipedia. Video.

6. Plane

Generally, all planes are used to flatten, reduce the thickness of, and impart a smooth surface to a rough piece of lumber or timber. Planing is also used to produce horizontal, vertical, or inclined flat surfaces on workpieces usually too large for shaping, where the integrity of the whole requires the same smooth surface. Wikipedia. Video. 

7. Hand saw 

In woodworking and carpentry, hand saws, also known as "panel saws", are used to cut pieces of wood into different shapes. This is usually done in order to join the pieces together and carve a wooden object. They usually operate by having a series of sharp points of some substance that is harder than the wood being cut. The hand saw is a bit like a tenon saw, but with one flat, sharp edge. Wikipedia. Video. 

Timber

Parts of a Tree 

The Trunk: The main stem of a tree, the trunk is the most important part of a tree for timber production.

The canopy (crown): this part of the tree is the uppermost part of the tree, made up of branches, stems, and leaves.

The roots are the part of a plant that attaches it to the ground or to a support, typically underground, giving water

and nourishment to the rest of the plant via numerous branches and fibres.

Inside of a Tree

Sapwood: most recent annual rings of a tree.

Cambium layer: growth area of a tree.

Heartwood: wood surrounding the core of the trunk.

Pith: central part of the trunk.

Growth rings: marks indicating the yearly growth of the trunk.

Bark: protective outside covering of the trunk.

How trees become timber

The trees are usually cut into smaller lengths on site and then picked up by a timber lorry, which transports

the timber to a processing site, such as a sawmill, paper mill, pallet, fencing or construction producer. At the

chosen site, the logs are debarked and bucked, or cut to the required length.

Different types of cuts

Plain Sawn

This cut of wood is common and is distinguished by its sawing method. The board is cut, turned 90

degrees then cut again. This cut also produces a minimal amount of waste.

Quartersawn

This cut of wood is distinguished by its grain pattern that runs vertically and has a straight, striped

appearance. Planks are cut by first dividing the log into quarters, then live sawing the wood. This cut has a higher

cost due to the manufacturing process and the lower yield of wood per plank.

Rift sawn

This cut of wood is the most expensive and least common. The planks are cut perpendicular to the tree’s growth

rings. This cut can provide a more modern look through the very linear grain pattern and is popular with oak and

maple species. However, it is difficult to get these types of planks wider than four inches across.

Defects in timber

Bow

When the converted timber is stored for a longer time, some timber planks may have a curve along its length, which

is known as Bow.

Wane

The edge part of the timber log contains a rounded edge on one side because of its original rounded surface. This

rounded edge is called wane.

Split

Split forms when a check extends from one end to the other end, which will split the wood into a number of pieces.

Twist

Twist forms when the timber piece is distorted spirally along its length. It looks like a propeller blade after twisting.

Chip mark

When the timber is cut through the planning machine, the parts of the machine may form chip marks on it.

Usually, they are indicated by chips on the finished surface.

Trees native to New Zealand

 

Kauri

Kauri is among the world's mightiest trees, growing to more than 50 metres tall, with trunk girths of up to 16 metres. 

Rimu

A slow growing tree that can grow up to 50m high. It is recognizable by it’s shaggy looking foliage resembling an

old man's beard.

Matai

Matai or black pine is an endemic New Zealand coniferous tree that grows on the North Island and South Island.