Triple families-Common Pythagorean Triples

Thursday, February 25, 2021

Pythagorean Triples

These Pythagorean triples are used with to find angles and side lengths. Common triples are 3,4,5 and 5,12,13 and 7.24,25, and 8,15,17, and 9,40,41.

These Pythagorean triples satisfy a^2 + b^2 = c^2
For example, let's use the triple 3-4-5
3 x 3 = 9, 4 x 4 = 16 5 x 5 = 25
9 + 16 = 25

Why learn these triples?
If you can recognize these triples it can make working right triangles much easier.
When you recognize two parts of the triple then you do not have to use trigonometric ratios to find the other leg or hypotenuse.

Pythagorean triples chart

Related Lengths

What are the three Domain of Life?

Wednesday, February 24, 2021

 The Earth has a amazing variety of Life

Variety of Life

However all Living organisms found on Earth can be divided into three large domains based on their characteristics.

The three domains are Bacteria, Archaea, and Eukarya.

3 domains of Life

Let’s take a look at some of the characteristics of each domain.

Bacteria and Archaea are the two domains made up of only single cell organisms.

They also contain only  prokaryotes which are organisms that have cells that do not contain a nucleus nor membrane bound organelles. 

However, even though they are similar they are also very different.

First the cell walls of bacteria and archaea are different. 

Bacteria have cell walls that contain peptidoglycan.

Archaea cells do not contain peptidoglycan in their cell wall.

bacteria vs archaea

Cells have membranes that surround them and allow materials in and out and separate them from their environment.

The plasma membrane of archaea use isoprene chains instead of a fatty acid chain which are found in bacteria.

The enzymes that read the genetic code in archaea are different than the enzymes that read the genetic code in bacteria.

To date no archaea have been known to cause disease in humans and they are able to survive in extremely harsh environments like hot springs and hydrothermal vents.

The domain Eukarya contains a huge variety of living organisms.

Eukarya organisms are both unicellular and multicellular

In addition, the cells of this domain are eukaryotic cells which means they contain a nucleus and membrane bound organelles like mitochondria

The kingdoms in this domain include,

Protists, Fungi,   Plants,  and Animals

Major domains

So in summary there are three major domains used to classify all organisms on Earth.

They are Bacteria, Archaea, and Eukarya.

Related Links

The Difference between Bacteria and Archaea

Monday, February 22, 2021


Why we have three Domains in classification

If you mention the name Carl Woes to most biology students, you may draw a blank stare. Carl Woes was a microbiologist at the University of Illinois. He championed the idea that organisms can be classified by looking at their genetic material. As a result, modern classification had a paradigm shift and added a third domain thanks to his work. Mr. Woes was the first to show how Archaea organisms are not bacteria nor a eukaryote but a completely different domain of organisms.

3 domains

Let’s take a look at how bacteria and Achaea are different.

One of the first things you will learn about archaea is that many live in extreme environments like deep hydrothermal vents, or in hot springs.

This is true but they can also be found living next to bacteria in your gut.

Archaea do share many similarities with bacteria which may cause you to think they are the same organism.

*They are single-celled organisms

*They do not contain a nucleus or membrane-bound organelles

*They reproduce asexually.

However, there are some important differences.

bacteria vs archaea

1.First, the cell walls of bacteria and archaea are different. 

Bacteria have cell walls that contain peptidoglycan (pep tuh dow glai kn) archaea cells do not contain peptidoglycan in their cell wall.

2.Cells have membranes that surround them and allow materials in and out and separate them from their environment.

The plasma membrane of archaea use isoprene chains instead of a fatty acid chain which are found in bacteria.

isoprene chain

3.The enzymes that read the genetic code in archaea are different than the enzymes that read the genetic code in bacteria.

4. I find this interesting, to date, no archaea are found to cause disease in humans some diseases we may get are caused by a bacterial infection.

As a result of these differences and several others, modern classification changed and a third domain was added and now we have three domains, bacteria, archaea, and eukarya.

Related Links

6 Kingdoms of Life

Bacteria Cell Structure

Types of Slope-Positive - Negative - Zero - Undefined

Tuesday, February 9, 2021


The slope of a line is a measure of the rate of change or steepness of a line. Slope is represented with the letter M

The slope of a line can be defined as the rise of the line over the run over a line.

negative slope
A line with a negative slope will go down from left to right.

In addition, as x increases y will decrease.

positive slope
A line with a positive slope goes up as you move from left to right.

As x increases y will also increase.

undefined slope
A line with an undefined slope will be vertical.

A y changes x will remain constant.

zero slope
A line with zero slope will be horizontal.

As x changes y will remain constant.

Related Links

Slope from a Graph

Adaptations in Biology Examples

Saturday, February 6, 2021

Adaptation Biology Examples

Did you know that dogs are actually descendants of wolves? Long ago, people began domesticating wolves, gradually transforming them from wild animals into hunting partners and companions. Through the domestication process, wolves adapted to live with humans. Though a shaking chihuahua is a far cry from a fierce wolf, dogs still possess many of the adaptations that allow wolves to thrive in the wild.    

Adaptations are traits that increase or decrease the fitness of an organism. In other words, adaptations either help or hinder the ability of an organism to survive. Adaptations are genetically controlled and therefore can be passed on to successive generations.

Let’s take a look at some examples of adaptations from different types of organisms.

Adaptations Snake

Adaptations can be sorted into three types.


For example, turtles have a hard protective shell.


Many animals travel in packs which help individuals alert others of danger.


Female mammals produce milk for their young which increases the chance of their offspring surviving.

desert plants

Desert plants live in a harsh environment where water is scarce. As a result, desert plants have many adaptations that enable them to collect or retain water efficiently. For example, some desert plants have short root systems that spread out over wide areas to collect as much water as possible during rain showers. Other desert plants have developed long tap roots that dive deep into the ground in search of water far beneath the surface. Most desert plants have waxy leaves that retain water inside the plant and prevent water from evaporating in the hot sun.

human body

The human body also presents many adaptations. For example, humans have a large number of sweat glands that allow us to cool off and survive in hot environments. In high altitude locations where oxygen levels are low, it appears that human bodies can evolve over time to use oxygen more efficiently. While most people would feel sick in the Tibetan mountains due to lack of oxygen, the bodies of the Tibetan people are oxygen-converting machines. 


A euglena is a single-celled protist. These little protists adapted to become mixotrophs, meaning they can act as an autotroph and a heterotroph. Autotrophs are capable of producing their own food from inorganic substances. Euglenas are photoautotrophs, which means they have chloroplasts that allow them to carry out photosynthesis and make food from sunlight. Heterotrophs, on the other hand, must eat other organisms for food. Euglenas are also classified as heterotrophs because they feed on living organisms, such as bacteria and algae. 


Sloths are famous for moving slow and hanging out in trees. They also have many adaptations that increase their fitness. For example, they have an extremely slow metabolism. Sloths' diet primarily consists of leaves. Leaves do not contain much energy, but a sloth’s slow metabolism enables the sloth to store energy from its food for long periods of time. In addition, leaves are hard to digest, but sloths have a complex stomach that breaks down and ferments leaves efficiently.


Owls are very successful birds of prey with many helpful adaptations. Here is a brief list: their feathers are designed for silent flight. Their eyes are full of rods which gives them extraordinary night vision. They have tufts that resemble twigs and branches and allow them to blend into their surroundings. Finally, they have the ability to turn their heads 270 degrees in each direction. You can’t sneak up on an owl!

Quick reminder: an adaptation is an inheritable trait that increases an organism's ability to survive and reproduce in its given environment. 


Cuttlefish are masters of camouflage. They practice adaptive camouflage which means they can change their color and texture based on their surroundings. Cuttlefish use specialized skin cells, called chromatophores, that act as color “pixels” on their skin and change the color and design of their body.


Tarantulas have the ability to use hairs on their abdomen as a defense mechanism. When tarantulas are attacked or feel threatened, they kick their back legs, sending the hairs on their abdomen hurtling towards their attacker. If successful, these barbed hairs will hurt and irritate the predator’s eyes and nose. 


Opossums have the ability to play dead. When attacked, they will act and even smell like a dead animal by laying on the ground and releasing a smelly fluid from their backside. The opossum appears stiff and lifeless which hopefully discourages attackers.

So, as a recap: dogs, which descended from wolves, still possess many of the characteristics that help wolves survive and thrive in the wild, such as a keen sense of smell and good night vision. 

Desert plants have waxy leaves that keep water trapped inside the plant, enabling the plant to survive in extremely dry climates. 

A sloth’s slow metabolism enables it to conserve energy from its leaf diet. 

Cuttlefish use specialized skin cells, called chromatophores, to blend into their surroundings and hide from predators. 

The characteristics of these animals have something in common: they help the animal survive in its environment and give the animal a chance to live long enough to reproduce. These helpful characteristics are called adaptations.

Related Links

Biomes of the World

Longest living insect pet

Three Domains of Life

5 Types of Air Masses

Wednesday, February 3, 2021

What is an air masses?

An air mass is a large mass of air in which temperature and humidity are the same throughout.

For an air mass to form the air must stay over the area long enough to pick up the characteristics of the area.

types of air masses

Air masses are named after where they are formed.

A maritime air mass forms over water and are moist and is represented with a lowercase m.

A continental air mass forms over land and are dry and is represented with a lowercase c.

In addition, an air mass is named by its temperature.

A tropical air mass is warm and is represented with a capital T.

A polar air mass is cold and is represented with a capital P.

An arctic air mass is very cold and is represented with a capital  A.

naming an air mass

How is an air mass named?

An air mass contains two names.

The first name is always lower case and describes where it formed and the amount of moisture the air mass contains

The second name is capitalized and describes the temperature of the air mass.

5 types air masses

Types of air masses

Continental Air Masses

A cT  air mass is a continental Tropical which means it will form over land, and will contain dry and warm air.

A cP air mass is a continental Polar and is dry and cold.

A cA or cAA is a continental artic or continental Antarctica and are dry and very cold.

Maritime Air Masses

A mP air mass represents a maritime polar air mass and forms over water and will be moist and cold.

A  mT air mass represents a maritime tropical are mass which are warm and moist.
A maritime equatorial and very warm to hot and very humid.

Air masses move around the Earth by Global winds and the Earth's jet streams.

Related Links

All about Global Winds

Thursday, January 28, 2021

Global Winds

In ancient times, sailors realized that certain winds are always present at certain locations of the Earth. In fact, many sailors became rich by using the trade winds to travel from one city to another. Why do we have these winds on Earth?

Tilt of the Earth Global winds

Due to how the earth tilts on its axis, the sun's rays strike Earth at different angles. This results in unequal heating of the earth’s surface. For example, the equator receives more direct sunlight than places such as the Arctic pole. This is why the equatorial region is so much warmer than the Arctic and Antarctic poles.  

Cold air is denser than warm air. It sinks, creating high-pressure areas.

Warm air is less dense and rises, creating low-pressure pockets. 

Air will always flow from high-pressure areas to low-pressure areas. 

Because the earth spins, anything that floats above the earth’s surface (such as air) appears to follow a curved pattern of movement. This is called the Coriolis Effect. The Coriolis Effect heavily impacts the travel pattern of global winds. 

In the northern hemisphere, air moving from north to south deflects to the left. From the equator to the poles, air deflects to the right.

Coriolis effect

Now, let’s put all of this together and look at some global winds.

First, we will label the Earth.

The direction of the Global winds change every 30 degrees on Earth.

You can see I have the Earth labeled 90, 60, 30, and 0 degrees in the northern and southern hemispheres.

Global Winds

At 90 degrees, the air is very cold and dense and creates a high-pressure system. At 60 degrees, the air is warmer, resulting in a low-pressure system. At 30 degrees, the air is cooler than it is at the equator, creating a high-pressure system. It is very hot at the equator and the warm air creates a low-pressure area once again.  

Notice the alternation between high-pressure and low-pressure areas. Every 30 degrees witnesses a pressure change. 

Next, remember that the Coriolis Effect heavily impacts air flow. Wind systems will twist clockwise or counterclockwise under the Coriolis Effect. In fact, this is what happens with prevailing winds. 

There are three main prevailing wind belts: the Prevailing Westerlies, the trade winds, and the Polar Easterlies. 

polar easterlies

The Polar Easterlies are the dominant winds found between 60 degrees of latitude and the poles of the earth. Remember that air likes to move from high-pressure areas to low-pressure areas. So, the wind will start from the poles at 90 degrees, areas of high pressure, and move down towards 60 degrees, where the pressure is low. 


The Prevailing Westerlies are the dominant winds found between 30 degrees and 60 degrees of latitude, and the Coriolis Effect moves them from west to east. 

Hint: Winds are always named from the direction that they start from.

trade winds

The trade winds will move from the high-pressure area of 30 degrees towards the equator, which has low pressure. This air will move down from the high pressure at 30 degrees and curves to the left because of the Coriolis Effect. The trade winds are also called the Tropical Easterlies because they blow from east to west.

Are there areas with little wind?

The doldrums, also called the Intertropical Convergence Zone, is such a place. At the equator, the air is very warm due to direct heating from the sun. Remember, hot air rises, and since the equator receives such intense sunlight, the air at the equator rises vertically like a hot air balloon instead of blowing horizontally.

As a result, the doldrums, which are located between 0 degrees and 5 degrees of latitude, experience very little wind. 

all about Global Winds

The horse latitudes, located at 30 degrees north and south, also experience little wind. The horse latitudes are areas of high pressure and thus, winds go separate ways from one another, searching for pockets of low pressure. The prevailing westerlies will head towards 60 degrees of latitude while the trade winds will head towards the equator. Sailors tried to avoid areas like the doldrums and the horse latitudes because they wanted strong winds that would push their boat along.

Related Links

Local Winds

Mountain and Valley Breezes

Air Masses

Powered by Blogger.
Back to Top