The Most Beautiful Mathematical Formulas

With around 50 formulas, this is a must for future mathematicians. 5/5!

Part 1: Powers of Numbers (Form. 1-2)
This very concise part explains about the powers of numbers (any number!) Also, it explains that (x^n)(x^m) = x^(n+m).

Part 2: Tri., Rect., Squ., and Cir. (Form. 3-10)
This part contains the innovative geometric discoveries. Things such as the areas of geometric figures, the rediscovery of the Pythagorean Theorem, and equal proportions in which rearrangement of areas of a square doesn’t make a difference.

Part 3: Angles (Form. 11-15)

This section talks about the proportion of the sine of an angle to its cosine. Also, it explains how the number pi (3.1415926535897932384626433832795...) is approximately 355/113, despite the fact that pi is irrational.

Part 4: Quadratic Equations (Form. 16-18)
It explains the Golden Ratio used in quadratic equations, the roots of a quadratic equation, and imaginary numbers. This is again a very concise part.

Part 5: Logarithms and Exponentials (Form. 19-28)
It describes the discovery of logarithms, how to find logarithms, the number e, that number raised to real and imaginary power, and that e to the i*pi power=-1.

Part 6: Series of Numbers (Form. 29-34)
This is probably one of my most favorite sections in the book. It has paradoxical equations, such as ½+¼+1/8+1/16..., the Fibonacci Sequence, permutations, 1+2+3+…_+n= n(n+1)/2, and more.

Part 7: Objects in Space (Form. 35-39)
This explains the theories about 3-D figures like cubes, spheres, pyramids, and prisms. It contains the formula of the surface area and volume of a sphere. It also has Euler’s Theorem: the faces on a 3-D figure -the edges + the number of vertices (corners).

Part 8: Whole and Prime Numbers (Form. 40-44)
This is probably my favorite section out of the entire book. Lagrange’s Theorem explains that any number is the sum of four squares. More topics are the facts that prime numbers are indivisible except for itself and 1, the Goldbach’s Conjecture, stating that every even number (except 2) is a sum of two primes, and Fermat’s Last Theorem.

Part 9/10: Chance/ Today and Tomorrow… (Form. 45-47, 48-49)
These two sections are so concise that they can be summarized in one whole piece. It has the chance of winning the lottery, Pascal’s Triangle, betting on roulette, the binary system, and the book-ender: the concept of infinity.

I hope you find this book somewhere and enjoy it! That’s all for now!

An Inconvenient Truth

Today, I will review the book that would surely change the minds of global warming skeptics, An Inconvenient Truth, written in 2006 by the former Vice President of the USA, Al Gore.

This book has fascinated me tremendously about what is going to happen in the next century, and how we can prevent that from happening.

It explains a lot of interesting facts about global warming and its effects on our planet. It first talks about the changing Earth and what caused this transformation. The cause is not natural, but reflects our indifference towards our own planet by the sorry ways we treat our environment. These ways include the burning of fossil fuels, deforestation, and, most importantly, greenhouse gas (primarily CO2) emissions. It also explains how global warming occurs.

I also made a diagram on Paint in my computer explaining how this happens.

As we go on, we see the effects of this climate change by looking at comparisons of past and present pictures of places such as the Swiss Alps, Glacier National Park in Montana, and Mt. Kilimanjaro in Tanzania. The snow and the glaciers have partly, or even completely melted, making a clear difference in the pictures.

The impact of global warming at the North and South Poles is explained as well, stating that parts of those areas are showing unmistakable signs of global warming. Chunks off the western Antarctic shelf have broken off from the huge continent made of ice. Natural species, such as the emperor penguin at Antarctica, or the polar bear of the Arctic, are facing certain extinction unless we are able to reverse these effects.

Because the sea level might rise 20 feet if Greenland’s entirety or the eastern Antarctic shelf had melted, maps might be redrawn, especially in the case of coastal areas. New York City’s Manhattan streets might be underwater if that happened, and so would major world cities like Miami, Amsterdam of the Netherlands, Calcutta of India, parts of Bangladesh, and most of the low-lying Oceania.

Global warming can cause infectious creatures/carriers (along with their diseases) to spread to areas previously a “Do Not Enter” zone. Take the West Nile virus in the US, it completely spread through the Lower 48 in just 5 years. Also, the season for most animals to hunt has changed.

With all this, you may think it’s impossible to reverse this effect. But you CAN. It won’t be immediate, but we can do it, but only if we don’t keep on doing these things.

Facts to know:

The USA is the area that produces the most CO2. Our Chlorofluorocarbons (CFCs) use has dipped from 1987 onward, preventing new ozone holes from forming.
Two advanced countries haven’t ratified the Kyoto Protocol yet: Australia and the USA. Many US cities, however, are abiding to the Kyoto Protocol.

This transfers a message throughout the reading world: global warming is devastating, but with cooperation, global warming can be reversed.

The Wind in the Willows

My 14th book that I have read, continuing my reading marathon from last Tuesday is The Wind in the Willows by Kenneth Grahame. It is filled with the adventures of four animal friends, going from one part to the next. 5/5!

Here is the summary of the book:

During spring cleaning, Mole decides not to clean his house and decides to go outside and breathe the fresh air. He greets the Water Rat, who is rowing his boat. The two decide to have a picnic near the Wild Wood, a place where a good mix of animals live. After the picnic, Mole tries to row the boat, but he doesn’t have much success.

Over the next few months, Mole has learned how to row the boat. The two decide to meet Toad, who is very rich and lives in a mansion named Toad Hall. They ride a horse-drawn cart, but soon, a motorcar zips right by them, causing the cart to tip over.

After this incident, Toad pursues the thought of driving a car. After the incident that leaves Rat angry at the driver, Mole wanders into the Wild Wood and gets chased into a hole in a tree. Rat soon finds him and the two stay at the Badger’s home in the heart of the woods.

The atmosphere was soothing as it melted away Rat’s and Mole’s chills from the cold, snowy weather. Mole and Rat decided to go on a hike, but shortly returned to Mole’s house. A group of field mice carolers spent the night at Mole’s house.

After that, the Badger joins the two to go to Toad Hall to settle his obsession with cars. However, Toad’s cleverness makes the three go to the village, allowing him to escape. He later steals a car and was apprehended and in the process gets one year for stealing a car, three more for careless driving, and fifteen more years for arguing with the police.

The judge sentenced him for 19 years, but he immediately rounded it off to 20. The jailer’s daughter became Toad’s caretaker. Together they hatched a plan to escape to disguise Toad in the caretaker’s aunt’s washing clothes. He snuck out of the jail and quickly boards the last train of the day, only to find that a police train was in hot pursuit of them. Both escaped without harm and Toad finds a barge, but a rude comment from the other passenger causes him to get off.

He rides his old horse and gets six shillings and all the food that the gypsy he met had to offer (all this in return for his horse). Toad sees the car that he had stolen. He offers to drive, but rude comments from the two other men causes him to drive carelessly again.

Mole and Rat attempt to find Little Portly, a child that always runs off. They find him between one of the hooves of a beast with a melodic pipe. Rat meets the Sea Rat and he tells Rat his voyages at sea. Rat was highly interested as the Sea Rat told his stories.

Toad is shocked that weasels and ferrets had taken over Toad Hall. Rat tells him about the invasion and how some of his friends disguised themselves and snuck in (such as Mole dressing up in a washwoman’s suit). Toad is angry at all this and wants to get even with the weasels and ferrets.

The four sneak into the house through an underground secret passage. They took the weasels by surprise and fended off the entire weasel and ferret troop. They had invited many friends to a party at Toad Hall the next night. Rat told him not to be boastful in order for the party to be a good one. The animals wanted him to do so, but he simply said no. They thought that Toad had gone through a change (and a good one, too)!

A Pocket Guide to WEATHER

Today, I take a break from the 5-day fictional marathon and focus on a non-fiction book, continuing my reading marathon. The book is called A Pocket Guide to Weather. It covers all things from climate change to types of precipitation to disastrous weather to the future climates. 5/5!

Section by section, here are the summaries:

Section I (11 pgs.)
This section is about both weather and climate, but mostly climate. It explains the nine different climates of the world: tropical, subtropical, temperate, arid, semi-arid, Mediterranean, mountainous, sub-arctic, and polar.

Section II (59 pgs.)
This section is the longest out of all of the sections in this book. It explains the global weather patterns, clouds, seasons, and the types of weather. Further detail of those subjects gives us topics such as warm/cold/occluded fronts, the jet stream, air pressure, the water cycle, types of clouds, and precipitation in all forms (rain, snow, hail, fog, etc.)

Section III (21 pgs.)
This section explains about weather patterns, but this time these are local patterns. It contains explanations of continental and maritime climates, oceanity, altitude, winds, pollution, and wind chill. The last pages are about animal adaptations to different types of environment such as the temperate, polar, arid (desert), and tropical environments.

Section IV (36 pgs.)
This section explains about violent types of weather. You can already think of the topics right now. To check yourself if you’ve covered the types, these extreme types of weather are thunderstorms, hurricanes/cyclones/typhoons, tornadoes, waterspouts, floods, heat waves, droughts, bush fires, and snow-related weather (avalanches, blizzards, hailstorms, etc.)

Section V (10 pgs.)
This may seem the shortest section in the book, but it is not. Anyway, this section is about weather opticals.
If you don’t know what I mean, these should help you, Mirages, rainbows, coronas, auroras, and haloes all count in this chapter.

Section VI (15 pgs.)
This section is about the history of weather and also the beliefs of ancient peoples about weather. Descriptions include the invention of the Celsius scale, beliefs about weather gods, Robert Fitzroy, early weather devices, 20th century weather devices, and weather involved in warfare and the performing arts.

Section VII (17 pgs.)
This section explains today’s weather forecasting methods. Subjects of this chapter include the usage of radar and satellite, thermometers, barometers, anemometers, monitoring precipitation, and the broadcasting of weather forecasts.

Section VIII (8 pgs.)
This section is by far the shortest section. It explains about how people use and manipulate the weather. Topics include cloud “seeding” and how people use the weather using renewable resources. Breaking down into the renewable resource topic, we get the use of sunlight, water, and air for energy. Of course, almost everything in life has a downside. The section explains the impact of the usage of these methods of energy.

Section IX (11 pgs.)
This section explains the climates of the past. These topics are simply the Paleozoic/Mesozoic eras, the Ice Age, the “Little Ice Age” and the Milankovitch Cycles.

Section X (30 pgs.)
This section was the most interesting to me because this explains the future climates. It explains climate change, El Niño and La Niña, acid rain, CFCs, more storms, heat waves, global dimming, and disease spreading due to global warming. All of them can happen (and some of them have already happened) if we keep using fossil fuels and adding to the greenhouse effect. This is the most appealing to me because I don’t want the world to be affected severely by global warming.

This book is a must for those who are learning about weather, but you can also read it for enjoyment.

Here’s a way more precise rating for this book: infinity out of infinity!

Books

So far, I have only read 10 books out of a collection of around 30 books (even though they are not the only books I have read). Those 10 books were (the most recent at the top):

Journey to the Center of the Earth- Jules Verne
The Legend of Sleepy Hollow/Rip Van Winkle- Washington Irving
Peter Pan- J. M. Barrie
The Time Machine- H. G. Wells
Moby Dick- Herman Melville
The Call of the Wild- Jack London
Oliver Twist- Charles Dickens
The Adventures of Sherlock Holmes- Sir Arthur Conan Doyle
The Adventures of Tom Sawyer- Mark Twain
20,000 Leagues Under the Sea- Jules Verne

I enjoyed every single book, except for two of them. It’s a 1 in 45 chance that you’ll guess the two.

Now for the summaries.

Journey to the Center of the Earth

In the mid-1800s, a professor named Otto Liedenbrock, brings his nephew, Alex, to Iceland to try and reach the center of the Earth. Hans Bjelke, their guide, goes with them as they embark on a spectacular journey that involves intense heat, rapid currents, and real-life dinosaur-era creatures. It ends when they are forced out by an eruption that lands them in Sicily, to the south of Italy. They return home, and Alex marries his love, Gretchen.

The Legend of Sleepy Hollow/Rip Van Winkle

Ichabod Crane, a schoolmaster in Sleepy Hollow, tries to win the heart of his love, Katrina Van Tassel. But his rivals, Brom “Bones” and his gang, try to humiliate him and marry Katrina. One night after a party, he returns home, only to find the Headless Horseman, the legendary ghost of a Hessian soldier from the Revolutionary War, chasing him out of the thick forest! He tries to outrun him on his horse, Gunpowder. But Gunpowder’s saddle slips and he is not able to hold on to his horse. The Headless Horseman flings his ”head”, which is kept at the right of him, to Crane. It hit his own head and later, Ichabod Crane, dies. Brom Bones ends up marrying Katrina, and laughs whenever he hears the Crane story.

In a New York settlement, near the Catskill Mountains, Rip Van Winkle goes exploring and finds three people bowling. He drinks something beer-like, and falls asleep for 20 years. He wakes up, confused about the new atmosphere. He later finds out that the colonists have won independence against the British and formed a new country, the United States of America.

Peter Pan
The Darling family kids, Wendy, John, and Michael, find Peter Pan in their room as they go to Neverland, a place that only exists in imagination. They embark on many different adventures, but most of all, they fight the pirates, led by Captain Hook. Wendy, John, and Michael use clever tactics with the help of Peter to take down the pirates and return to the real world.

The Time Machine

A man claims to have made a time machine, but other men do not believe him. However, the Time Traveler travels to the future and discover that the human race had split into two groups, the Morlocks and the Eloi. At one point he loses his time machine and goes on a long search for it, looking in bushes, near trees, and in ancient buildings. He finds in inside a pedestal with a winged figure on it and returns to the present day.

Moby Dick

An ordinary man joins the crew of a whaling ship, the Pequod, and finds that the captain of the ship, Ahab had a grudge against a large white whale named Moby Dick because he lost a leg against him. His crew had took down many whales on their journey, but Moby Dick sank the ship. Many of the sailors drowned, but a few of them survived.

The Call of the Wild

Buck, a wolf-like dog from California, is taken to the freezing northern lands and becomes a sled dog. The dogs ran many miles and suffered from tiredness and hunger. Some of the dogs died. But not Buck. He had great endurance, and he even killed the strong leader, Spitz. Buck replaced him as leader. But after many miles, three dogs remained. Buck ran away from the pack because he had heard a wild wolf’s “call of the wild”. The native people are afraid to enter a specific area because of abnormal wolf tracks created by Buck’s spirit.

I will say my piece on the last 4 books on the list next time. However, I can tell you that all 10 books are great stories to read, and that you can picture each in your mind. That is why these books are enjoyable.

Sneak Preview: The next two books that I will read might be Alice in Wonderland, The Adventures of Huckleberry Finn and The Wonderful Wizard of Oz. There will be updates about all the other books as I read them.