Chapter II

                                                     Methodology         

          if all sides and angles of a polyhedron are equal, it is called a regular polyhedron. The Intraoctagon formed in this mathematical investifatory project is a regular polyhedron. Having its equal sides, the volume of Intraoctagon was determined.

            The Octagonaal prism’s face was drawn on a cartesian plane. The vertices and medians were assigned by using the pythagorean theorem, which states that a triangle with an internal angles of 45-45-90 have 1 in its 2 adjacent sides of 90 and  in its hypothenus. Each side was assigned as 2a. The vertices were connected to the medians opposing it. The connected vertices to medians were called exclusive medians. The slopes of the exclusive medians were computed to determine the equation of the lines. After getting the slopes of the exclusive medians, the line equations were obtained using the slope and point in point slope formula. After getting the equation of the lines, ellimination method was used to determine the intersections or the new vertices for the intraoctagon. The distance formula was used to prove that the distances  of the vertices formed inside were equal. the method of ratio and proportion was used to get the volume of the intraoctagon to the volume of the regular octagonal prism. The derived formula for the intraoctagon was obtained by deriving the formula of the regular octagon’s volume by using the side of the new intraoctagon. 

Am I Aware?

                    Having regrets in life is normal and usual. Making things unexpectedly may bring good things that can make you happy and making bad things unexpectedly may lead you to regret it and blame yourself. Regrets in life make lessons and new beginnings. There's no exact predictions to know if the thing that you do is going to be good and not to regret.


                    When I was elementary, I just go to school to study. Sometimes I get perfect score in our test, finish the seatworks faster than my other classmates and I was able to answer correct in recitations. When I reached the Intermediate elementary, my lost of concentration in study started. I had my "barkada" and influenced me to play only. Playing makes me happy, but, I didn't notice that I lost my concentration to my studies and got low grades. Until now, it's happening to me and sometimes I tell "O life, why you're so playful?". Sometimes I blame myself on this things that I've done, the things that doesn't make sense destroyed me. I feel angry to myself every time I remember that. Those memories that are left are marks of mistake.


                     All of that things that i have done was not a big deal for me now. "Life has no ending, only new Beginnings", thats what I always remember whenever I've done wrong. If I let my mistake take me to a worst then It make no sense and It will just stop me from getting my goals. When I regret of something, I think of another way to contrast it.

“Sometimes I wish life was written pencil so we could erase it and write it all over again.” 
― Thisuri Wanniarachchi, COLOMBO STREETS

Being Special is something Special

              Being special starts from the day we were fertilized as a zygote up to a baby. We are special when we're born. It makes us special because in thousands or millions of sperm cells, you're the one that was born and live a life on earth. Parents treat us special and care for us every time. Also someday, there's someone that will treat us special like our own parents and he/she will be the partner in life.

              Am I special? yes, I am, and everyone is special. What makes me special? my friends can trust me, my friends can rely on me, my friends can seek for a help from me, I can make them happy in my OWN way. Being unique and different to another individual is not noticeable. Each one of us is Special and unique. In Twins, they are just look alike in physical appearance but you can't tell if they're alike also in attitude. I am a special one. There might be Ira or Valentin with a surname of De joys or Hernandez, there might be a Ira Valentin H. De Joya Jr. or Ira Valentin H, De Joya III , but , there's only me, Unique in personality and in name, Unique in physical appearance and attitude.

               Treating oneself as special good. Other people thinks that they're not special and they're useless in these world, but, it's not true. Its just their thoughts that makes them feel not special. You can make legacy and be an outstanding person if you strive harder.

3rd Year memories

                  In my 3rd High School life it was a bit hard and happy in the beginning. We are just moving from 2nd year life last school year. This feeling is not new anymore, I experienced this before when I'm going to be a high school. It was hard also to adjust, but I was different experience.

                  In my Junior Life, I experienced to have new subjects, new friends and new goals. In early junior life, It was a bit hard to learn higher level of sciences and mathematics. I experience new good things and bad things. I was also hard to adjust to my new classmates that I met. I experienced to commute with my former classmates and I don't have service anymore, which I feel that I am independent. I experienced to be the champion in Rubik's cube in Math Fest and champion in Division MTAP friendly games. I was my dream to reach that goals that I never expected to happen. In our English subject, I became the Romeo of our group in Romeo and Juliet play. I was nervous because I was not used into acting, I felt bad on what I did, but, It turned out something nice. We also had our Jazz chant and it is by class activity. Other activities like radiodrama and Oration was also done last gradings. We also had our conventional speech choir which I think is our best, we became first and got 25% in the test just like the other section. These are all great experiences.I feel to be In love again and gain new experiences. About the bad things, I got low grades which I don't like, I strived harder for the 3rd grading but it's not enough. I got also an exemption in Finals in Math and Geom, I am Really HAPPY for that.

                  Being a Junior wasn't bad, It makes me realize that next year in senior life it's our turn to graduate. Our batch is the last batch of 3rd years because next year it will be grade 9. Just Enjoy being a High school and someday we will miss being in a high school life and being a Junior. These experiences and memories that was done in my junior life is memorable.These memories will be a treasure for us someday and can be an inspiration to the next generation. "Knowledge without experience is useless" for me.

A sorry for marie

084 B San Francisco St.

Tanza, Cavite

February 10, 2014

Dear Cleo,

                It was almost a year ago since we became friends, I thought that we will not be friends. It was like a blink and I never expected that we will be friends. You look like 'masungit' for me and I am so quiet like I'm afraid of you. 

                Sometimes It's my fault that's why I feel irritated to you and sometimes your fault. I don't even have the guts to say the bad way I feel to you. I am idolizing you because your good at designing, you're good at handwriting and you're also good in speaking with rhyme. Also, sometimes I hurt your feelings unintentionally and unexpected, i am sorry. 

              I really don't know how to end your bad feelings to me, but this is for the things I've done to you that I regret. The things that hurt your feelings, I want to say sorry. It is not my intention to make your feelings worst for me. I didn't expect that I do that. I am really SORRY.

Your friend,

Ira Valentin

A prayer for my parents

Dear God,

Since I was a kid, I am not fully appreciating my parents that much. I just playing with my toys but still I love my parents. Without my parents then there will be no “me”. That time i can’t express my feelings to them and I was used to that way. 

I am blessed with my parents who is there for me. Until now, I am not expressive but I appreciate them always on what they do to us. Sometimes I help them with their task because I am already a teenager and not a child. At first of being a teenager, It seems like they are still treating me like a child but for a teenager I don’t like to be a child anymore and i want to be independent. Sometimes, I get angry but I realize that I don’t need to be angry in small things.

Now, I can’t say even “I love you” except only if there’s an occassion in our family or they are the one who say it first. My parents always say to me that I should study well for my future. I am always thinking of that and they want me to get a better life and work than they have today. 

For thanking them, dear God, Let me finish my studies and have a good job to support them in the future like they did to me. I pray that my future my family will appreciate me as I appreciate my parents for what they done.

A Son

Conversation with my Idol

I dreamed that someday I can talk to my Idol from the past and this day became true. I feel nervous at the same time I'm excited. I didn't think of anything but him. I'm thinking on what I'm going to say and ask to him. I feel the happiness inside me as he come closer to me.

Ira:  Uhm. Good day Mr. Erno Rubik. I'm glad to meet you.

Mr. Erno: Good day to you also. What's your name? you look so happy.

Ira: Mr. Erno my name is Ira from philippines. I want to ask some important things that you did.

Mr. Erno: Ohh. Ira but it's a girls name. By the way, what would you like to ask to me I'm willing to answer those questions.

Ira: Yeah. its a girls name. I would like to ask what leads to the construction of the rubik's cube?

Mr. Erno: I was an Architect, Designer and a University professor. In 1974, I created the first working prototype of the cube.

Ira: How it became so popular?

Mr. Erno: in 1975, I named it as a "magic cube" and hungarian toy-manufacturer - politechnika begins the mass production. It was first sold in Budapest toyshop in Hungary in 1977. The "magic cube" was renamed and become "Rubik's cube" and it was exported by the Ideal toy corporation.

Ira:  How about the solution to that puzzle the 3x3x3 cube? who made the solution for the puzzle?

Mr. Erno: In 1981, A 12 year old boy from England produced a book entitled "You can do the Cube" by Patrick Bossert. The book goes on and sold about 1.5 million copies of it. It contains the algorithms to solve the cube.

Ira: When was the first competition held? How many cubes was sold?

Mr. Erno: The first annual International Rubik's Championship competition are held in Budapest in Hungary in 1982. Over 100 million cubes have been sold. Another One, The Rubik's enter in the Oxford english dictionary

Ira: Oh, It was so many cubes. What have you reached through this career?

Mr. Erno: I became the president of the Hungarian Engineering Academy. I established the International Rubik Foundation to support talented young designers. Diamond cutters International created the first "masterpiece cube" for the Rubik's cube 15th birthday. The cube was fully functional and was made from a solid gold and encrusted with colored jewels and it is 185 carat cube.

Ira: WOW! a cube made from gold and jewels. I think it is very expensive. I wish I can be like you. As of now, what are you going to do?

Mr. Erno: Now, I'm enjoying my retirement. The World Cube Association manage the competitions for speedcubing all over the world. The Rubik's Studio continues to design games and work with young designers in Hungary and beyond.

Ira: It was Awesome! I would like to join competitions someday since I can do speedcubing. That's all Mr. Erno Rubik Thank you for the time you gave to meet me. I hope you're also happy. I never expected this day to come.

Mr. Erno: It's Time to say Goodbye, I was happy that I answered your question. I hope that I help. See you next time.

Ira: Goodbye! Mr. Erno Rubik.

This time that I talked to my Idol, I was very happy like I reached the Nirvana. Even thought it is a short time, it doesn't matter at all.